Officials said yesterday that the White House and State Department were also likely to fight such a move as a breach of executive authority, making the appearance of the notes unlikely until they are published in a historical record decades from now.
So for now, everyone but Trump and Putin and perhaps a handful of their close confidants are in the dark.
Even Trump's own intelligence chief, Dan Coats, said yesterday, "I don't know what happened in that meeting".
"It is utterly amazing, utterly amazing, that no one knows what was said," Chuck Schumer, the top-ranking Democrat in the Senate, said. "This is a democracy. If your President makes agreements with one of our leading - if not our leading - adversary, his Cabinet has to know about it and so do the American people."
Typically, a summit, especially one between two major powers, will occur after weeks and months of meticulous planning at lower levels with an eye toward producing demonstrable results. Agenda topics, talking points, desired outcomes and even major portions of significant agreements are normally negotiated in advance so the relevant agencies of both countries are aware of any potential policy changes. In some cases, the actual summit meeting and leaders' signatures on a piece of paper or a joint communique are mere formalities as the hard work has already been done by subordinates.
Those conventions have been upended by Trump's buccaneering approach to affairs of state - the kind of approach he thinks worked in his landmark summit with North Korean leader Kim Jong Un last month. But this time there was no joint statement to formalise the outcome of the talks - just a meandering, 45-minute press conference where Trump stoked controversy by appearing to side with Putin over US intelligence agencies' assessment that Russia meddled in the 2016 election.
Russia's ambassador to the US, Anatoly Antonov, yesterday expressed hope that "the verbal agreements between Putin and Trump will be fulfilled" - though the substance of any such understandings remain murky, not least because the main business was conducted in the two hours of discussions between the two leaders with only translators joining them.
The Trump Administration yesterday poured cold water on at least one proposal from Putin: that Russia be allowed to interview Americans the Kremlin accused of crimes - the quid pro quo for allowing US investigators to interrogate Russian intelligence officials recently indicted in the US for alleged election interference.
"That's not going to happen," Secretary of State Mike Pompeo said of the Russian proposal in an interview with the Christian Broadcasting Network.
Still, from Putin's perspective, the summit put Moscow and Washington on "the path to positive change". In recent days he has spoken of finding broad consensus with Trump on ensuring security along Syria's border with Israel and on arms control issues. Russia's Defence and Foreign ministries, meanwhile, have both said they are ready to start putting those agreements into action.
Trump himself has also put a positive spin on the summit. He says a second meeting with Putin will usher in the implementation of the laundry list of items they discussed in Helsinki. Those, he said in a tweet, include terrorism, security for Israel, nuclear proliferation, cyberattacks, trade, Ukraine, Middle East peace and North Korea. "There are many answers, some easy and some hard, to these problems ... but they can ALL be solved!" he said.
Pressed for details, however, the White House could not provide any.
Press secretary Sarah Huckabee Sanders mentioned Syria, Iran, Israel, arms control, Russia's annexation of Crimea from Ukraine and its meddling in the 2016 US election as having been discussed. But turning those issues from topics of discussion into action apparently remains a work in progress.
"This is the beginning of the dialogue with Russia and our Administration and theirs and we're going to continue working through those things," she told reporters at the White House on Thursday.
Just minutes later, the State Department offered its own take on the Helsinki meeting, saying that no agreements were reached, just general proposals on matters mainly related to economic and strategic co-operation.
Spokeswoman Heather Nauert said three proposals were made: One for a high-level working group with US and Russian business leaders to be convened, another for the creation of an "expert council" of academics, current and former diplomats and military officials from both countries to look broadly at US-Russia relations, and a third one for the US and Russian national security councils to hold a series of follow-on meetings.
"You know, these are certainly all modest proposals," she said. "The President had said going into this that we wouldn't solve all the world's problems in one meeting, in one conversation with the Russian Government but we think it's a pretty good place to start."
At the Pentagon, officials were still waiting to see if their marching orders in Syria would change as a result of the summit.
The commander of US forces in the Middle East said yesterday that he had not received new guidance from the Pentagon on co-operating with Russia in Syria.
"We have received no further direction than we've currently been operating under," General Joseph Votel said in a video-teleconference from his headquarters in Tampa, Florida. He said he's taking a "steady-as-she-goes" approach in Syria in the absence of new instructions.
'That's going to be special'
Even Donald Trump's intelligence chief doesn't know what was said in the President's one-on-one meeting with Russian President Vladimir Putin in Helsinki.
Director of National Intelligence Dan Coats was also unaware that Putin was being invited to Washington.
Coats made those surprise admissions yesterday in his first public comments since rebutting Trump's questioning of the US intelligence assessment that Russia interfered in the 2016 election.
Speaking at the Aspen Security Forum in Colorado yesterday, Coats said he wished Trump had made different statements in Helsinki after meeting Putin.
Coats, who is charged with overseeing the nation's 17 intelligence agencies, also said that if he had been asked, he would have advised Trump against meeting Putin alone, with just interpreters.
As he spoke, news was breaking out of Washington that Putin had been invited to the White House this American fall. NBC's Andrea Mitchell, who was moderating the event, shared the development.
Coats said it was news to him.
"Say that again," Coats said, cupping his hand over his ear.
He took a deep breath and continued, saying: "Okay." He added: "That's going to be special," prompting laughter from the audience.
- AP