Most voters (57 percent of respondents) also agree that a special prosecutor should be appointed to investigate alleged ties between US President Donald Trump's campaign staff and the Russian government.
The poll comes in response to reports that several associates in Trump's campaign for the US presidency had contact with Russians, including Attorney General Jeff Sessions, who met with Russian Ambassador Sergey Kislyak despite testifying under oath that he never met with Russian officials before or after the election.
Trump has struggled to distance himself and his administration from the Russia-related controversy casting a cloud over the early days of his term.
In the speech, Mr Trump said an "easing of tensions and improved relations with Russia" are possible. The US candidate arrived to the reception area within a hotel, where he met with Ambassador Kislyak and other foreign officials.
Well into the second half of his nearly two-hour program Sunday night on the state-controlled Rossiya channel, commentator Dmitry Kiselyov blamed the mainstream US media for not allowing Trump even to talk about improving ties with Russian Federation. "To state a "meeting" took place is disingenuous and extremely misleading".
The CNN/ORC poll, which has a 3 percent margin of error, was conducted from Wednesday through Saturday on a random sample of 1,025 adults.
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The reports directly contradict the President's repeated denials about contact with Russian officials prior to his election.
Page, who has worked at Merrill Lynch in Moscow and says he has advised Russia's oil and gas giant Gazprom on "key transactions", has strongly denied the accusation that he served as a middleman between Trump's campaign and Russian Federation. The fact that Trump is now President rightfully calls into question the possibility that a Justice Department investigation will be tainted by political considerations, so there is definitely an argument in favor of appointment an ostensibly apolitical outsider, such as a long-serving career Justice Department attorney.
Since the beginning of Trump's term, these allegations have been widespread, ranging from allegations of hacked elections to former National Security Advisor Michael Flynn being forced to step down because of his contact with Russian officials.
According to news reports published at the time that have now resurfaced, Mr Trump met briefly with Vladimir Putin's representative in Washington around six months before polling day.
The Trump administration may want to change the topic and move on from these Russian Federation allegations, but Americans don't feel the same way. "I have nothing to do with Russian Federation", he said. Haven't made a phone call to Russian Federation in years.
"Russia is a ruse", Trump said at a February 2017 press conference.