The Republican majority leader spoke amid reports that Mr Trump had asked his then-FBI director, James Comey to drop an investigation into former National Security Adviser Mike Flynn.
"We can't deal with speculation and innuendo and there is clearly a lot of politics being played", he said. "It is obvious there are some people out there who want to harm the president, but we have an obligation to carry out our oversight regardless of which party is in the White House".
Speaking at a joint news conference with the visiting Italian prime minister, Putin said on Wednesday Moscow initially found debates about Russia's meddling in US politics as "funny" but said Moscow is now "concerned because it's hard to imagine what the people who produce such nonsense can come up with next".
Russian President Vladimir Putin has dismissed the ongoing scandal around President Donald Trump sharing classified intelligence with Russian officials as "political schizophrenia".
He cited the current investigations by congressional intelligence committees and House Oversight Committee Chairman Rep. Jason Chaffetz's request for transcripts and tapes of Trump's conversations.
The House speaker said he still has confidence in Trump.
The request came after The New York Times revealed on Tuesday the existence of a memo Comey had written showing Trump's attempt to obstruct the FBI's Russian Federation investigation. "The point is this", the speaker said when asked about the controversy at a press conference on the Hill Wednesday morning. In addition Trump is facing pointed questions about his discussions with Russian diplomats during which Trump is reported to have disclosed classified information. Trump himself said he had "an absolute right" as president to share "facts pertaining to terrorism" and airline safety with Russian Federation.
Comey's memo, an apparent effort to create a paper trail of his contacts with the White House, would be the clearest evidence to date that the president has tried to influence the investigation.