The president said he thought the ousting would be greeted with bipartisan support.
Trump fired Comey as head of the FBI last week, saying the dismissal was driven by a loss of faith in the bureau chief on behalf of both himself and the public.
In a statement, the White House said "the president has never asked Mr. Comey or anyone else to end any investigation involving General Flynn".
Monmouth University Poll surveyed a pool of 1,002 adults between May 12 and 17.
"No, no. Next question", he said, speaking at a press conference with the Colombian president. Trump made the surprise move of firing Comey, head of an investigation into Trump and his campaign's alleged ties with Russian Federation, early last week.
One senior European intelligence official told the Associated Press his country may curb its intelligence sharing with Washington for fear of what Trump could reveal to Russian officials.
Putin's remarks came after Washington Post reported late Monday that Trump jeopardized a critical source of intelligence on the terror group Daesh during a May 10 meeting with Russian Foreign Minister Sergey Lavrov and Ambassador Sergey Kislyak at the White House.
Russia has repeatedly said that anti-Russian politicians in the United States are using groundless fears of closer ties with Moscow to sabotage any rapprochement and damage Trump in the process. "I'm saying they raised an allegation and we have an obligation to look into them", Rubio said. Mr Trump said on national television last week that the Russian investigation, which he says is an attempt by Democrats to save face following an embarrassing electoral defeat, was a consideration in making the decision to can Mr Comey.
When Trump fired Comey, he said he did so based on Comey's very public handling of the Hillary Clinton email probe and how it affected his leadership of the Federal Bureau of Investigation.
The intervention by Putin could turn up the pressure on the White House to provide its own transcript of the meeting. The meal came on the same day Flynn was accused by House Oversight Committee Chairman Rep. Jason Chaffetz of Utah and Maryland Rep. Elijah Cummings of failing to disclose payments he had received from Russian Federation and Turkey. When that ended, Trump asked everyone to leave except Comey, and he eventually turned the conversation to Flynn.
Congressional Republicans have largely backed Trump through the rocky initial months of his administration, but the events of the past week - Comey's firing, the report that Trump disclosed classified information to Russian officials, and Comey's memo - are testing the party's patience. "If in fact what was said in the memo is true, it's very concerning and we need to get to the bottom of that".
Meanwhile, intelligence community veterans anxious that sharing intelligence gleaned from a USA ally without their permission could endanger sources on the ground and make countries less willing to share intel with Washington.