In his tweet, Trump also falsely asserts that there are no questions about "Collusion."
While the questions published by the Times are wide-ranging - and include more related to possible obstruction of justice - the list includes 13 related to possible cooperation between the Trump campaign and Russia.
Among those is a query about Trump's knowledge of any outreach by his former campaign chairman Paul Manafort to Russia "about potential assistance to the campaign." A court filing this month revealed that Mueller had sought authorisation to expand his probe into allegations that Manafort "committed a crime or crimes by colluding with Russian government officials".
Another question asks about Trump's knowledge of a June 2016 meeting in Trump Tower between his aides and a Russian lawyer who offered politically damaging information on Trump's Democratic opponent, Hillary Clinton.
And another asks what Trump knew about "Russian hacking, use of social media or other acts aimed at the campaign?"
In his tweet, Trump calls collusion "a phony crime" and repeats his claim that none existed. The president also derides Mueller's investigation as having "begun with illegally leaked classified information," adding: "Nice!"
That is a reference to notes that former FBI director James Comey provided to a friend documenting his interactions with Trump. The president has said that action, which prompted the appointment of a special counsel, amounted to illegally leaking classified information and that Comey should be imprisoned.
Comey, whom Trump fired last year, has said repeatedly that the information was not classified. He and Trump have been sparring over the issue as Comey continues a publicity tour to promote his new book, A Higher Loyalty, which portrays Trump as an ego-driven and congenital liar.
In a later tweet Tuesday morning, Trump wrote that it "would seem very hard to obstruct justice for a crime that never happened!"
But that, legal experts, say is a misunderstanding of the law.
"This is flat wrong," said Randall Eliason, a former assistant US attorney who teaches white-collar criminal law at George Washington University Law School.
"The purpose of the investigation is to determine whether a crime was committed, and, regardless of the ultimate answer to that question, it is a separate crime to attempt to obstruct that inquiry," Eliason said. "It's also true, of course, that we don't yet know that the underlying crime 'never happened.' "
Trump has said previously that he would be willing to have a face-to-face meeting with Mueller or his team, but more recently he has wavered on the prospect.
Rudy Giuliani, Trump's new personal lawyer dealing with the probe into Russian interference in the 2016 election, met with Mueller last week to reopen negotiations for a possible presidential interview.
Giuliani conveyed the ongoing resistance of Trump and his advisers to an interview but did not rule out the possibility, according to people familiar with the talks.
Raj Shah, a White House spokesman, said later Tuesday morning that White House officials are frustrated that much of Mueller's focus seems to be outside his original aim of investigating Russian interference in the 2016 election.
Appearing on Fox News, Shah said he couldn't speak to the accuracy of the questions published by the Times. But, he said, "if they are accurate, the overwhelming majority of those questions don't focus on the underlying premise of this special counsel."
