Nancy Pelosi said the US President had “ given reason to believe that this should be looked into”.
“I think it’s an abuse of power, and as far as obstruction of justice,” the House Democratic leader told US broadcaster MSNBC, adding that special counsel Robert Mueller “should look into this.”
Mr Mueller was appointed by the US Justice Department to oversee the investigation into Russian interference in the 2016 United States election.
Mr Comey, fired by the President last month, testified before a Senate committee that he believed Mr Trump had ordered him to end the probe into Mr Flynn's alleged ties to Russia.
Mr Flynn was forced to resign from his post in February after it was revealed that he had misled Vice President Mike Pence about his conversations with a Russian official.
In his opening statement, Mr Comey said the President had privately told him in the Oval Office a day after Mr Flynn's resignation: “I hope you can see your way clear to letting this go, to letting Flynn go. He is a good guy. I hope you can let this go.”
Ms Pelosi also criticised House Speaker Paul Ryan for appearing to excuse the President’s behaviour because he is “new” to government and may not know the relationships between the various branches.
The FBI director is a political appointee nominated by the president, and can be removed by the US leader at any time. However, the bureau is meant to be insulated from the political pressure of the White House.
Mr Comey had first recorded details of his interactions with the President in a series of memos.
After Mr Trump tweeted that there may be recordings of their conversations, Mr Comey said he felt the need to reveal his written account of their Oval Office meeting.
“So I asked a friend of mine to share the content of the memo with a reporter,” Mr Comey said during the hearing. The friend was later identified as Daniel Richman, a professor at Columbia Law School.
Mr Trump has accused Mr Comey of leaking information, writing in an early morning tweet the day after the hearing: “Despite so many false statements and lies, total and complete vindication...and WOW, Comey is a leaker!”
Ms Pelosi also said she has concerns about Mr Trump’s “fitness for office”, saying he needs more sleep.
Mr Trump has said that he sleeps very little, only about four to five hours a night. He also has a habit of launching Twitter attacks in the early hours of the morning.
When asked about what advice she’d give Mr Trump on how to become a stronger leader, Ms Pelosi said she has advised him to “get some sleep.”
“Bring yourself to a place where the synapses are working,” she added.
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