"We had a very, very successful meeting with the foreign minister of Russia, our fight is against ISIS," Trump said Tuesday, after making a statement alongside Turkish President Recep Tayyip Erdogan after their bilateral meeting.

"As Gen. (H.R.) McMaster said -- I thought he said and I know he feels -- that we had actually a great meeting with the foreign minister, so we are going to have a lot of great success over the coming years and we want to get as many to help fight terrorism as possible and that is one of the beautiful things that is happening with Turkey. The relationship we have together will be unbeatable," the President said.

Earlier Tuesday, the White House insisted that Trump did not risk national security by sharing classified information with top Russian officials and revealed the President did not even know the source of the intelligence he divulged.

According to US and diplomatic officials, Israeli intelligence was a source for some of the information about ISIS bomb-making capabilities that the President discussed with Russian diplomats.

Israel's ambassador to the United States, Ron Dermer, would not comment on the intelligence but expressed confidence in the US-Israel relationship.

"Israel has full confidence in our intelligence sharing relationship with the United States and looks forward to deepening that relationship in the years ahead under President Trump," he said.

The White House would not comment on Israel being the source, but spokesman Sean Spicer said he was "obviously pleased" with Dermer's comments.

'Wholly appropriate'

National security adviser H.R. McMaster said that Trump's behavior at the Oval Office meeting last week was "wholly appropriate" after The Washington Post first reported that the President revealed top secret information that had been passed to the United States by a foreign intelligence service.

"The premise of that article is false, that in any way the president had a conversation that was inappropriate or that resulted in any kind of lapse in national security," McMaster said, as he launched a frantic damage control effort in the White House Briefing Room.

But the national security adviser did not specifically deny key aspects of the story, which said the President had shared details of an ISIS plot to bomb civilian airlines in a way that could allow Russia to trace the source of the intelligence.

He would not confirm that the information in question came from a foreign intelligence partner. But he pushed back at the suggestion that the incident could prompt overseas intelligence services to think twice about sharing intelligence with the US.

McMaster also said Tuesday that Trump himself wasn't fully aware of important context surrounding the intelligence he disclosed to Russian officials, implying Trump didn't realize the gravity of his disclosure.

"The President wasn't even aware of where this information came from," McMaster told reporters. "He wasn't briefed on the source."

Trump, who appears increasingly under siege and unable to control the trajectory of his presidency amid multiple self-inflicted crises, was defiant, insisting in a Twitter post that he had made a strategic decision to share intelligence with the Russians, reportedly about an ISIS terror plot targeting civilian airliners with a new generation of laptop bombs.

"As President I wanted to share with Russia (at an openly scheduled W.H. meeting) which I have the absolute right to do, facts pertaining to terrorism and airline flight safety, Humanitarian reasons, plus I want Russia to greatly step up their fight against ISIS & terrorism," Trump tweeted Tuesday.

As President I wanted to share with Russia (at an openly scheduled W.H. meeting) which I have the absolute right to do, facts pertaining.... — Donald J. Trump (@realDonaldTrump) May 16, 2017

...to terrorism and airline flight safety. Humanitarian reasons, plus I want Russia to greatly step up their fight against ISIS & terrorism. — Donald J. Trump (@realDonaldTrump) May 16, 2017

Trump is correct that a President has the authority to disclose classified information. But his explanations yet again appeared to undercut the efforts of his own team to put out a blazing public relations crisis.

Hurried improvisation

In a sign of the hurried improvisation in the West Wing, McMaster brought up plans to brief the press by several hours to 11:30 a.m. ET.

A White House official said McMaster's briefing was intended to "calm Republicans on the Hill," and moved up by two hours in an effort to slow the flood of GOP questions and criticism over the Russian intelligence flap.

"I stand by my statement that I made yesterday," he told reporters at the White House. "The premise of that article is false."

McMaster said everything Trump discussed with Lavrov and the Russian ambassador to the US was appropriate to the setting.

"In the context of that discussion, what the President discussed with the foreign minister was wholly appropriate to that conversation," McMaster said.

Inside the West Wing, officials don't yet know how Trump believes McMaster did, since he's been tied up with Erdogan meetings.

An official says the President's reaction will become clear by whether he tweets again about this, or tries to let McMaster have the final word.

A source with knowledge about the tense internal dynamics of the West Wing told CNN's Gloria Borger that the President's son-in-law and senior adviser Jared Kushner had expressed frustration with the communications shop over the handling of the President's sudden firing of FBI Director James Comey last week -- even though Trump's team had little advance notice of the stunning move.

The latest bewildering developments in the White House raised questions about Trump's competency and an administration which appears locked in a perpetual cycle of ever escalating instability.

It also reignited the controversy over Trump's relationship with Russia, which has been accused of meddling in last year's election to help him win. And it left intelligence chiefs considering whether Trump's decision to share highly sensitive information received from a foreign intelligence source with a US adversary could endanger American lives by halting the flow of top secret information from abroad.

The uproar also compounded the political damage inflicted on the administration by Trump's sudden dismissal of Comey a week ago.

Borger's source, who speaks with Trump, describes a commander in chief who feels under siege, blames his staff and is thinking about next steps to get his administration back on track.

Trump "seems to have lost confidence in just about everybody," the source said.

JUST WATCHED Sen. Corker: White House in a downward spiral Replay More Videos ... MUST WATCH Sen. Corker: White House in a downward spiral 00:46

GOP reaction

The magnitude of the political headache facing the White House is reflecting in increasingly critical positioning from top GOP lawmakers.

John McCain, chairman of the Senate Armed Services Committee, released a strikingly critical statement about Monday's developments.

"The reports that the President shared sensitive intelligence with Russian officials are deeply disturbing. Reports that this information was provided by a US ally and shared without its knowledge sends a troubling signal to America's allies and partners around the world and may impair their willingness to share intelligence with us in the future," McCain said.

"Regrettably, the time President Trump spent sharing sensitive information with the Russians was time he did not spend focusing on Russia's aggressive behavior, including its interference in American and European elections, its illegal invasion of Ukraine and annexation of Crimea, its other destabilizing activities across Europe, and the slaughter of innocent civilians and targeting of hospitals in Syria," McCain said.

House Speaker Paul Ryan notably did not come out forcefully in favor of the President Monday night, issuing a statement seeking more information.

In his first reaction, Senate Majority Leader Mitch McConnell made the point on Tuesday that all the turbulence unleashed by the White House was jeopardizing grand Republican plans to exploit congressional majorities.

"I think we could do with a little less drama from the White House," McConnell said on Bloomberg Television. "We could focus on our agenda, which is the regulations, tax reform, repealing and replacing Obamacare."

On Monday Sen. Bob Corker, the chairman of the Senate Foreign Relations Committee warned that the White House was "in a downward spiral right now" and staff "have got to figure out a way to come to grips with all that's happening."

JUST WATCHED Panetta: Trump needs grown-ups around him Replay More Videos ... MUST WATCH Panetta: Trump needs grown-ups around him 02:28

Intelligence questions

As the intrigue over the intelligence dimensions of the latest White House controversy deepened, it has emerged that administration officials contacted the intelligence community following last week's meeting between Trump and top Russian officials in the Oval Office, to check on the classification level of items he discussed.

The concern was raised by Homeland security adviser Thomas Bossert, according to an administration source. Bossert, who was not in the meeting, read a classified summary of the discussion and realized that the plot was discussed. Bossert felt the intel community needed to know what was said, according to the source.

The information was brought up by Trump spontaneously, the source said. When the President brought up the classified information, he did it in the context of trying to push the Russians to be helpful with bad actors like Assad in Syria, the official explained.

A separate administration source explained that after the meeting between Trump and the Russians, the President's advisers checked on the specific classification level of information discussed in the Oval office meeting.

But the administration official insisted that no one involved in the meeting expressed alarm regarding the President's comments, which reportedly focused on an ISIS plot to bring down civilian airliners.

The intelligence behind the US ban on laptops and other electronics is considered so highly classified that CNN, at the request of US government officials, withheld key details from a previous story on the travel restrictions.

The concern, US officials told CNN, was that publishing certain information, including a city where some of the intelligence was detected, could tip off adversaries about the sources and methods used to gather the intelligence.

There is some disagreement, according to one of the sources, as to how far the President went. The intelligence relates to what is known as a special access program, or SAP, which covers some of the most classified information and is protected with unique access and security protocols.

According to The Washington Post , Trump described details to Lavrov and Kislyak about how ISIS hopes to use laptop computers as bombs on planes.

"I get great intel. I have people brief me on great intel every day," one official with knowledge of the meeting described Trump as saying, according to the Post, before the President reportedly relayed specific intelligence.

Details about how the White House responded to the meeting with the Russians emerged as Washington tried to digest the scale of the crisis now gripping the White House over last week's meeting.

Lawmakers, including prominent Republicans, are expressing concern about the President's actions and demanding more details from the White House, as broader debate rages over what the episode means for future US intelligence cooperation with foreign powers, and whether efforts to thwart the ISIS plot may have been complicated in some way.

McMaster branded the reporting "false" on Monday night as part of a swift White House damage control operation.

But Trump appeared to contradict his own staff and validate at least some of the reporting on Tuesday when he suggested the decision to talk to the Russians about the issue had been a strategic choice.

Two former officials knowledgeable about the situation confirmed to CNN that the main points of the Post story are accurate: The President shared classified information with the Russian foreign minister.

Trump's tweets Tuesday notably lack any mention of whether the information he shared was classified.

But Leon Panetta, a former secretary of defense and CIA director, said Trump had a responsibility to be more careful with sensitive information.

"He is President of the United States. He is not a reality TV star. He is not just another personality. He is President of the United States," he said Tuesday on "New Day."