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“What the president discussed with the foreign minister was wholly appropriate to that conversation and is consistent with the routine sharing of information between the president and any leaders with whom he’s engaged,” McMaster said at a White House briefing, seeking to play down the sensitivity of the information Trump disclosed.

McMaster added that the president, who he said was unaware of the source of the information, made a spur-of-the-moment decision to tell the Russians what he knew.

But McMaster also appeared to acknowledge that Thomas P. Bossert, assistant to the president for homeland security and counterterrorism, had called the CIA and the National Security Agency after the meeting with the Russian officials. Other officials have said that the spy agencies were contacted to help contain the damage from the leak to the Russians.

McMaster would not confirm that Bossert made the calls but suggested that if he did, he was acting “maybe from an overabundance of caution.”

“I have not talked to Mr. Bossert about that, about why he reached out,” McMaster said.

Former officials said it was not uncommon for presidents to unintentionally say too much in meetings and said that in administrations from both parties, staff members typically established bright lines for their bosses to avoid crossing before such meetings.

Israel’s concerns about the Trump White House’s handling of classified information were foreshadowed in the Israeli news media earlier this year. Newspapers there reported in January that U.S. officials warned their Israeli counterparts to be careful about what they told the Trump administration because it could be leaked to the Russians, given Trump’s openness toward President Vladimir Putin.