Asked if she felt more reluctant to share secrets with the United States now, May said decisions about what Trump discussed with people were "a matter for President Trump" and that Britain would continue to work with and share intelligence with the U.S.
Putin sent a defiant statement to those casting suspicion over Trump's attitude to Russia Wednesday, accusing them of being detrimental to the US itself.
But he made no mention of Trump divulging intelligence to Russian Federation that a U.S. administration official said had originally come from Israel. Either US officials would have to admit that the Russians had been allowed to record the meeting, with their knowledge, which would have looked bad; or they would have to deny it, which would have looked worse if there did indeed turn out to be a recording.
Vladimir Putin said on Wednesday that U.S. President Donald Trump had not divulged any secrets during a meeting in Washington with Russian officials and offered to prove it by supplying Congress with a transcript.
"If the U.S. administration deems it possible, we are ready to provide the Senate and Congress with the transcript of the conversation between Lavrov and Trump", Putin said at a press conference, following a meeting with Italian Prime Minister Paolo Gentiloni on Wednesday.
Social media was lit over the offer from the Russian president.
Speaking at a press conference in Sochi, Russia, Putin dismissed allegations that Trump had shared top-secret security intelligence with Russian diplomats as "political schizophrenia". "It's credibility would be less than zero".
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In Washington, Republican and Democratic lawmakers said they wanted to see the Comey memo.
"It may cause small damage - or local damage - but not a disaster", Sofrin said.
"As President I wanted to share with Russian Federation (at an openly scheduled W.H. meeting) which I have the absolute right to do, facts pertaining to terrorism and airline flight safety", Trump wrote in a series of early morning Twitter posts. "If we have really lost a human source over there, it's a major loss and it will take years to regenerate another one", he said.
"It's hard to imagine what else can these people who generate such nonsense and rubbish can dream up next", said Putin.
"What surprises me is that they are shaking up the domestic political situation using anti-Russian slogans".
"They either don't understand that they are harming their country - which makes them just dumb - or they understand, which makes them risky and dirty".
May said the government has confidence in its relationship with the United States, and will continue to share intelligence with Britain's most important defense and security ally.
The Kremlin isn't commenting on the details of the classified information that President Donald Trump shared with the Russian foreign minister and the Russian ambassador last week.