Asked if she felt more reluctant to share secrets with the USA 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.
The revelations sent a White House accustomed to chaos reeling anew and drew rare serious criticism of the president from some Republicans.
U.S. President Donald Trump, right, meets with Russian Foreign Minister Sergey Lavrov at the White House in Washington on Wednesday, May 10, 2017.
The White House has played down the importance and secrecy of the information President Trump gave to the Russians, which had been supplied by Israel under an intelligence-sharing agreement.
Speaking to CNN before reports emerged that Israel may be the source of the intel, former Israeli spymaster Danny Yatom said the revelation of classified intelligence by Trump "is a very disturbing issue and might cause a lot of danger". "This is not how a White House should operate", Schumer said.
"I have great confidence in our alliance", Turnbull said.
It is reported the president told Russian Foreign Minister Sergey Lavrov and Ambassador Sergey Kislyak classified information.
Other countries, including Arab allies, also supplied some intelligence that drove the United States to impose restrictions on laptops and other electronics on flights from 10 countries in the region.
"As president I wanted to share with Russia which I have the absolute right to do", Mr Trump tweeted on Tuesday, a day after the New York Times and Washington Post reported that he had shared highly classified information with the Russian foreign minister and Russian ambassador to the United States in a White House meeting last week. Other officials have said that the spy agencies were contacted to help contain the damage from the leak to the Russians. The official spoke on condition of anonymity because the official was not authorized to speak publicly. "He wasn't briefed on the method or source of information".
In a pair of tweets Tuesday morning, Trump insisted he had the right to share information with Russian Federation related to terrorism and other issues.
The Kremlin dismissed the reports of Trump's actions as "complete nonsense".
On Capitol Hill, Democrats and Republicans alike expressed concern. Sen.
Gallagher said last week that he was concerned by the timing of Trump's firing of FBI Director James Comey, who had overseen an investigation into Russian interference in last year's US election. To know that this intelligence is shared with others, without our prior knowledge? "I think it's important to investigate these sorts of things".
Steven Aftergood, a government secrecy specialist with the Federation of American Scientists, told the Washington Post, "It is an expression of presidential authority, and that means that the president and his designees decide what is classified, and they have the essentially unlimited authority to declassify at will".
McMaster refused to confirm whether the information the president shared with the Russians was highly classified.
According to the Washington Post story, what the president discussed with the Russians was under a code word.
Leon Panetta, a former secretary of defense and Central Intelligence Agency director, said Trump had a responsibility to be more careful with sensitive information. It's hard to imagine why McMaster would add the caveat about "not already publicly known" unless Trump had, contra Tillerson, discussed military operations.