Quizzed about the latest scandal in America, the Prime Minister said only that she had "confidence in the relationship between us and the United States - that it helps to keep us all safer".
The turmoil overshadowed Republican legislative priorities such as healthcare and tax reform and laid bare sharp divisions between the White House and USA intelligence agencies, which concluded late previous year that Russian Federation had tried to influence the 2016 presidential election in Trump's favor.
The link to Israel was first reported by the New York Times a day after it was disclosed that Trump gave Russian Foreign Minister Sergei Lavrov intelligence about a laptop bomb threat and revealed the Syrian city where the information was collected.
At the press conference in Sochi, Putin made light of the allegations.
According to sources cited in the report, that intelligence came from a U.S. ally who had not authorised Washington to pass it on to Moscow.
The White House immediately hit back at the report, denying its account of events.
"I spoke to him [Lavrov] today", said Mr Putin with a smile.
The paper said Mr Comey had documented what he saw as Mr Trump's improper efforts to influence him.
Mr Flynn was sacked by the president in February after he failed to disclose a conversation with the Russian ambassador to the United States.
Putin slammed critics who spread allegations about Trump's ties with Russian Federation.
Mark Warner of Virginia, top Democrat on the Senate intelligence committee, said he would ask Comey for additional material as part of that panel's investigation.
"Working with the USA and others to deal with the terrorist threat is an important part of maintaining our national security, and we will continue to do so", she added.
Trump weighed in personally the morning after his secretary of state, Rex Tillerson, and national security adviser, H.R. McMaster, issued statements saying no sources, methods or military operations were discussed at the Russian meeting. He used that phrase nine times in his briefing to reporters.
An Israeli spy's life is at risk as the result of US President Donald Trump's reported passing of classified information to senior Russian officials last week, ABC news reported Tuesday. "This is not a truthful or accurate portrayal of the conversation between the president and Mr Comey".
A US official who confirmed the disclosure to The Associated Press said the revelation potentially put the source at risk.
Defending Trump's actions, officials played down the importance and secrecy of the information, which had been supplied by Israel under an intelligence-sharing agreement, and Trump himself said he had "an absolute right" as president to share "facts pertaining to terrorism" and airline safety with Russian Federation.