The poll of 1,005 adults, conducted two days after the Helsinki meeting, is in stark contrast with Trump's assessment that the meeting was a rousing success and that those who disagree are "haters".
Addressing a joint press conference with his Russian counterpart at the Presidential Palace in Helsinki after their summit, Trump had said that there was "zero collusion" and that he ran a "clean campaign".
Russian Federation annexed the peninsula of Crimea in 2014. Ukraine has offered the regions autonomy under its rule.
Parts of the regions that are controlled by Russia-backed separatists - the rebel "people's republics" of Donetsk and Luhansk - held their own referendums in May 2014 and declared independence from Ukraine.
"The sentence should have been: 'I don't see any reason why it wouldn't be Russian Federation, '" he said.
Bloomberg said Putin was proposing a ballot of residents on the status of the two territories, carried out under global auspices.
If Coats had been in Washington instead of the conference, he would have been informed about the plan, one source familiar with the inner workings of the White House said on condition of anonymity.
The Russian ambassador said Moscow is ready to discuss a proposed new meeting between Putin and Trump, Interfax said. Putin has maintained that it was held in "strict compliance with global law", reiterating during the summit, "This case is closed for Russian Federation". "For us, the case is closed", he said.
Last month Trump appeared to leave the door open to the United States recognising the annexation. "Well, we saw earlier this week in Helsinki what was truly an Orwellian moment". It wasn't just the words he "misspoke" at the Helsinki summit that sparked criticism.
U.S. Director of National Intelligence Dan Coats and White House Social Media Director Dan Scavino (rear) listen during a cabinet meeting at the White House in Washington, U.S., July 18, 2018.
Members of the Senate Foreign Relations Committee said Friday they plan to revive a non-binding resolution that failed to pass this week and that would have put the chamber on record as supporting the intelligence community and its findings that Russian interfered in the 2016 election. "The first step was made, let's wait for the results now".
Putin told the channel: "We talked about Ukraine".
Russia's ambassador to the US, Anatoly Antonov, said in Moscow that the summit was a "remarkable event ... the main event of the current political season". "Look at the diplomats I threw out", Trump said.
And Sanders created a fresh headache for the administration when she said the White House was still reviewing a proposal from Putin to allow access by Russian law enforcement officials to Americans whom the Kremlin accuses of unspecified crimes in return for USA access to interrogations of Russian agents indicted for their alleged roles in interfering in the 2016 election.
Moscow welcomed the invitation with enthusiasm. Such a meeting would be another step towards discussing and resolving problems between the two countries, he said.