The statement, issued to the New York Times as it prepared an article, emphasised that the subject of the meeting was "not a campaign issue at the time".
The claims were later shown to be misleading.
Over the next three days, multiple accounts of the meeting were provided to the news media as public pressure mounted, with Trump Jr. ultimately acknowledging that he had accepted the meeting after receiving an email promising damaging information about Hillary Clinton as part of a Russian government effort to help his father's campaign.
The extent of the President's personal intervention in his son's response, the details of which have not previously been reported, adds to a series of actions that Trump has taken that some advisers fear could place him and some members of his inner circle in legal jeopardy.
As special counsel Robert S. Mueller III looks into potential obstruction of justice as part of his broader investigation of Russian interference in the 2016 election, these advisers worry that the President's direct involvement leaves him needlessly vulnerable to allegations of a coverup.
"This was . . . unnecessary," said one of the President's advisers, who like most other people interviewed for this article spoke on the condition of anonymity to discuss sensitive internal deliberations. "Now someone can claim he's the one who attempted to mislead. Somebody can argue the President is saying he doesn't want you to say the whole truth."
Trump has already come under criticism for steps he has taken to challenge and undercut the Russia investigation.
He fired FBI Director James B. Comey on May 9 after a private meeting in which Comey said the President asked him if he could end the investigation of ousted national security adviser Michael Flynn.
Director of National Intelligence Daniel Coats told associates that Trump asked him in March if he could intervene with Comey to get the bureau to back off its focus on Flynn.
In addition, Trump has repeatedly criticised Attorney General Jeff Sessions for recusing himself from overseeing the FBI's Russian investigation - a decision that was one factor leading to the appointment of Mueller. And he has privately discussed his power to issue pardons, including for himself, and explored potential avenues for undercutting Mueller's work.
Although misleading the public or the news media is not a crime, advisers to Trump and his family told the Washington Post that they fear any indication that Trump was seeking to hide information about contacts between his campaign and Russians almost inevitably would draw additional scrutiny from Mueller.
Trump, they say, is increasingly acting as his own lawyer, strategist and publicist, often disregarding the recommendations of the professionals he has hired.
"He refuses to sit still," the presidential adviser said. "He doesn't think he's in any legal jeopardy, so he really views this as a political problem he is going to solve by himself."
Trump has said that the Russia investigation is "the greatest witch hunt in political history," calling it an elaborate hoax created by Democrats to explain why Clinton lost an election she should have won.
Because Trump believes he is innocent, some advisers explained, he therefore does not think he is at any legal risk for a coverup. In his mind, they said, there is nothing to conceal.
[Trump's legal team faces tensions - and a client who often takes his own counsel]
The White House directed all questions for this article to the President's legal team.
One of Trump's attorneys, Jay Sekulow, declined to discuss the specifics of the President's actions and his role in crafting his son's statement about the Russian contact. Sekulow issued a one-sentence statement in response to a list of detailed questions from the Post.
"Apart from being of no consequence, the characterisations are misinformed, inaccurate, and not pertinent," Sekulow's statement read.
Trump Jr. did not respond to requests for comment. His lawyer, Alan Futerfas, told the Post that he and his client "were fully prepared and absolutely prepared to make a fulsome statement" about the meeting, what led up to it and what was discussed.
Asked about Trump intervening, Futerfas said, "I have no evidence to support that theory."
He described the process of drafting a statement as "a communal situation that involved communications people and various lawyers".
Peter Zeidenberg, the deputy special prosecutor who investigated the George W. Bush administration's leak of CIA operative Valerie Plame's identity, said Mueller will have to dig into the crafting of Trump Jr.'s statement aboard Air Force One.
Prosecutors typically assume that any misleading statement is an effort to throw investigators off the track, Zeidenberg said.
"The thing that really strikes me about this is the stupidity of involving the President," Zeidenberg said.
"They are still treating this like a family-run business and they have a PR problem . . . What they don't seem to understand is this is a criminal investigation involving all of them."
Advocating for transparency
The debate about how to deal with the June 2016 Trump Tower meeting began weeks before any news organisations began to ask questions about it.
Kushner's legal team first learned about the meeting when doing research to respond to congressional requests for information. Congressional investigators wanted to know about any contacts the President's son-in-law and senior adviser had with Russian officials or business people.
Kushner's lawyers came across what they immediately recognised would eventually become a problematic story. A string of emails showed Kushner attended a meeting with a Russian lawyer at Trump Tower in the midst of the campaign - one he had failed to disclose. Trump Jr. had arranged it, and then-campaign chairman Paul Manafort had also attended.
To compound what was, at best, a public relations fiasco, the emails, which had not yet surfaced publicly, showed Trump Jr. responding to the prospect of negative information on Clinton from Russia: "I love it."
Lawyers and advisers for Trump, his son and son-in-law gamed out strategies for disclosing the information to try to minimise the fallout of these new links between the Trump family and Russia, according to people familiar with the deliberations.
Hope Hicks, the White House director of strategic communications and one of the President's most trusted and loyal aides, and Josh Raffel, a White House spokesman who works closely with Kushner and his wife, Ivanka Trump, huddled with Kushner's lawyers, and they advocated for a more transparent approach, according to people with knowledge of the conversations.
In one scenario, these people said, Kushner's team talked about sharing everything, including the contents of the emails, with a mainstream news organisation.
Hicks and Raffel declined to comment. Kushner attorney Abbe Lowell also declined to comment.
The President's outside legal team, led by Marc Kasowitz, had suggested that the details be given to Circa, an online news organisation that the Kasowitz team thought would be friendly to Trump. Circa had inquired in previous days about the meeting, according to people familiar with the discussions.
The President's legal team planned to cast the June 2016 meeting as a potential setup by Democratic operatives hoping to entrap Trump Jr. and, by extension, the presumptive Republican nominee, according to people familiar with discussions.
Kasowitz declined to comment for this article, as did a Circa spokesman.
Consensus overruled
Circumstances changed when the New York Times began asking about the Trump Tower meeting, though advisers believed that the newspaper knew few of the details. While the President, Kushner and Ivanka Trump were attending the G20 summit in Germany, the Times asked for White House comment on the impetus and reason for the meeting.
During breaks away from the summit, Kushner and Ivanka Trump gathered with Hicks and Raffel to discuss Kushner's response to the inquiry, according to people with knowledge of the discussions. Kushner's legal team joined at times by phone.
Hicks also spoke by phone with Trump Jr. Again, say people familiar with the conversations, Kushner's team concluded that the best strategy would be to err on the side of transparency, because they believed the complete story would eventually emerge.
The discussions among the President's advisers consumed much of the day, and they continued as they prepared to board Air Force One that evening for the flight home.
But before everyone boarded the plane, Trump had overruled the consensus, according to people with knowledge of the events.
It remains unclear exactly how much the President knew at the time of the flight about Trump Jr.'s meeting.
The President directed that Trump Jr.'s statement to the Times describe the meeting as unimportant. He wanted the statement to say that the meeting had been initiated by the Russian lawyer and primarily was about her pet issue - the adoption of Russian children.
Air Force One took off from Germany shortly after 6pm - about noon in Washington. In a forward cabin, Trump was busy working on his son's statement, according to people with knowledge of events. The President dictated the statement to Hicks, who served as a go-between with Trump Jr., who was not on the plane, sharing edits between the two men, according to people with knowledge of the discussions.
In the early afternoon, Eastern time, Trump Jr.'s team put out the statement to the Times. It was four sentences long, describing the encounter as a "short, introductory meeting".
"We primarily discussed a programme about the adoption of Russian children that was active and popular with American families years ago and was since ended by the Russian government, but it was not a campaign issue at the time and there was no follow up," the statement read.
Trump Jr. went on to say: "I was asked to attend the meeting by an acquaintance, but was not told the name of the person I would be meeting with beforehand."
Over the next hour, word spread through emails and calls to other Trump family advisers and lawyers about the statement that Trump Jr. had sent to the Times.
Some lawyers for the President and for Kushner were surprised and frustrated, advisers later learned. According to people briefed on the dispute, some lawyers tried to reach Futerfas and their clients and began asking why the President had been involved.
Also on the flight, Kushner worked with his team - including one of his lawyers, who called in to the plane.
His lawyers have said that Kushner's initial omission of the meeting was an error, but that in an effort to be fully transparent, he had updated his government filing to include "this meeting with a Russian person, which he briefly attended at the request of his brother-in-law Donald Trump Jr".
Kushner's legal team referred all questions about the meeting itself to Trump Jr.
The Times' story revealing the existence of the June 2016 meeting was posted online about 4pm Eastern time. Roughly four hours later, Air Force One touched down at Joint Base Andrews. Trump's family members and advisers departed the plane, and they knew the problem they had once hoped to contain would soon grow bigger.
Alice Crites contributed to this report.
