(CNN) Members of President Donald Trump's own party are privately alarmed at his demeanor this week and his apparent lack of understanding of the consequences of his Syria policy , according to a Republican source familiar with a recent White House meeting.

This comes as top congressional Republicans have publicly broken with the President in recent days over the administration's move to withdraw US forces from Syria, and after a contentious Wednesday meeting at the White House.

A Republican source with knowledge of the meeting told CNN that participants were "shell-shocked" by the President's behavior adding, "Republican members were shaken by what they saw and heard" from Trump.

The source went on to tell CNN that the President's conduct was unsettling. "He is not in control of himself," the source said. "It is all yelling and screaming."

CNN has reached out to the White House for comment on this description.

But publicly, the top House Republican offered a different assessment. House GOP leader Kevin McCarthy, who was also at the meeting, called it "productive" and said Trump made clear that his main priority is to "make sure America is safe." The California Republican criticized House Speaker Nancy Pelosi's decision to leave the meeting, saying that the speaker had opted to politicize the event.

Texas Rep. Michael McCaul, the top GOP member on the House Foreign Affairs Committee, called it an "important meeting" and said that "it was very disappointing to see the Democratic leadership walk out of this meeting. I've never seen this before in my tenure in Washington."

Pelosi told reporters after the meeting that Trump had "a meltdown" and said at a news conference on Thursday that the President didn't like the questions she was asking about his foreign policy. According to Republican sources familiar with the meeting, the California Democrat's description was accurate.

The meeting took place shortly after the House of Representatives rebuked the President by passing a bipartisan resolution opposing his decision to pull US troops from northeastern Syria, a move that cleared a path for Turkey to attack US-allied Kurdish forces.

Asked what it was like in the room during the meeting, the Republican source told CNN, "It was bad from the moment he walked in," adding that it seemed like the House vote to approve the resolution "set him off."

"I have never seen anything like it. No one in the room has ever seen anything like it," the source said.

White House press secretary Stephanie Grisham described the meeting differently, saying in a statement on Wednesday that Trump was "measured" and "decisive" and that Pelosi "had no intention of listening."

"The President was measured, factual and decisive, while Speaker Pelosi's decision to walk out was baffling, but not surprising," Grisham said.

The President's Syria policy has opened a rare rift between Republicans and the White House that comes at a critical time for Trump's presidency as he faces down a House Democratic-led impeachment inquiry

Senate Majority Leader Mitch McConnell, a Kentucky Republican, who usually avoids criticizing the President, took the unusual step of saying on Thursday that he wants the Senate to pass a resolution condemning the move that is "even stronger" than the one that passed in the House.

Republican Sen. Lindsey Graham of South Carolina, who frequently defends the President, has publicly clashed with him this week, telling CNN on Wednesday that "He's not listening to his advisers."

"He's making the biggest mistake of his presidency by assuming the Kurds are better off today than they were yesterday," Graham said.

Republican Rep. Adam Kinzinger also expressed pointed criticism of the administration on Wednesday.

"Wow," Kinzinger tweeted in response to a Wall Street Journal report stating that "the U.S. military said two F-15E jet fighters carried out an airstrike to destroy an ammunition-storage facility, latrines, tents and other parts of the Syria headquarters of the US campaign to destroy Islamic State after pulling its forces from the base."

"We bombed our own base on purpose, because of the impulsive decision by @realDonaldTrump didn't leave time to evacuate the right way," the Illinois congressman tweeted. "Is this the America you grew up believing in?"

The situation in Syria shifted again on Thursday as US Vice President Mike Pence announced that he and Turkish President Recep Tayyip Erdogan had agreed to a five-day ceasefire halting Turkey's incursion into northern Syria.

But the deal appears to secure Turkey most of its military objectives, forcing America's onetime allies in the fight against ISIS -- Kurdish forces -- to cede a vast swath of territory, with one senior US official very familiar with operations in Syria telling CNN that the deal meant the US was "validating what Turkey did and allowing them to annex a portion of Syria and displace the Kurdish population."

And the move generated some Republican pushback, with GOP Sen. Mitt Romney of Utah, who has shown a willingness to criticize Trump over other issues, saying, "The announcement today is being portrayed as a victory. It is far from a victory."

"At the heart of this matter is a central question of why these terms and assurances were not negotiated before the President consented to withdraw our troops," Romney said.