By Stephen Collinson and Jim Sciutto

CNN

(CNN) -- The crisis-battered White House battled to avert what one top GOP senator warns is a "downward spiral" on Tuesday, following reports that President Donald Trump divulged highly classified information to two top Russian visitors to the Oval Office.

Rising concern and mystification among senior Republicans on Capitol Hill about the chaos raging at the White House added to the administration's struggle to explain the President's actions in his meeting last week with Russian Foreign Minister Sergey Lavrov and Moscow's ambassador to Washington Sergey Kislyak.

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.

He 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.

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

"I stand by my statement that I made yesterday," McMaster 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.

McMaster appeared alone, not as scheduled with White House spokesman Sean Spicer, who has been criticized by top Trump aides over his performance. Spicer will appear later, off-camera, to speak with White House reporters at 2 p.m. ET.

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.

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."

Republican Sen. Marco Rubio, a member of the Senate Foreign Relations Committee, said he had been in touch with the White House after the Post story broke on Monday, but needed more information.

"We need to learn more about it ... I have very specific questions and hope they will be answered at some point today," Rubio told CNN.

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."

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.

An 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."