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Senate Minority Leader Chuck Schumer, House Speaker Nancy Pelosi and House Majority Leader Steny Hoyer announced at a news conference outside the White House on Wednesday that they had just walked out of a meeting with President Trump on Syria policy, after he apparently called Pelosi either a "third-rate politician" or "third-grade politician" and angrily suggested the Democrats probably appreciated communist Islamic State terrorists in the Middle East.

"What we witnessed on the part of the president was a meltdown, sad to say," Pelosi, D-Calif., remarked.

She said later, at the Capitol: "I pray for the president all the time, and I tell him that -- I pray for his safety and that of his family. Now, we have to pray for his health -- because this was a very serious meltdown on the part of the president."

A senior Democratic aide told Fox News that Trump began the meeting, which was ostensibly called by the White House, by remarking that "someone wanted this meeting so I agreed to it."  Trump also reportedly told Pelosi, "I hate ISIS more than you do," prompting Pelosi to respond, "You don't know that."

Trump then remarked, according to the senior source: "President Obama drew a red line in the sand [in Syria].  In my opinion, you are a third-grade politician." (Schumer, D-N.Y., told reporters he heard Trump use the term "third-rate politician.")

Pelosi forcefully reminded Trump that the House had recently overwhelmingly voted to condemn his Syria policy, the source said.

She also told Trump, "All roads with you lead to Putin," according to the source.

The source told Fox News that Trump made a big show of a pointed letter he sent last week to Turkey's president, but that Democrats were unimpressed -- as the letter was sent after Trump effectively green-lit Turkey's invasion of Syria, and apparently had no effect on curbing Turkish aggression.

As the Democrats walked out, Trump reportedly remarked, "I'll see you at the polls."

Another Democratic source familiar with the conversation told Fox News that Schumer started to read the president a quote from former Defense Secretary James Mattis from Sunday: "And, in this case, if we don't keep the pressure on, then ISIS will resurge. It's absolutely a given that they will come back."

According to the source, Trump cut Schumer off and responded that Mattis was "the world’s most overrated general. You know why? He wasn’t tough enough. I captured ISIS. Mattis said it would take two years. I captured them in one month."

Trump reportedly said fewer than 100 ISIS prisoners had escaped amid Turkish aggression and the U.S. troop pullback in the Middle East, and that the escapees were "the least dangerous" ones. Defense Secretary Mark Esper, according to the source, confirmed the president's number, but not that those terrorists were the least dangerous. "I don't know that," Esper told Schumer, the source recounted.

The meeting devolved into the president calling the speaker a name, the source said, noting that Trump was "quite nasty, so she stood up to go. She started to sit back down but Hoyer got her to go. Pelosi and Hoyer walked out of the meeting."

The source said Schumer stayed back for a minute to push Esper on whether the U.S. had specific intelligence that the Turks or Syrians definitely would guard the other ISIS prisoners. Esper reportedly said they didn't have any such reports.

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White House press secretary Stephanie Grisham dismissed the reports from the meeting.

"The President was measured, factual and decisive, while Speaker Pelosi's decision to walk out was baffling, but not surprising," Grisham said. "She had no intention of listening or contributing to an important meeting on national security issues. While democratic leadership chose to storm out and get in front of the cameras to whine, everyone else in the meeting chose to stay in the room and work on behalf of this country."

Trump, for his part, tweeted pictures of the meeting, including one showing Pelosi standing and pointing her finger at the president. Trump captioned the photo, "Nervous Nancy's unhinged meltdown!"

Schumer, standing alongside Pelosi at the news conference outside the White House, claimed the discussion fell apart while the politicians were discussing the president's pullout from Syria -- and that Trump had said that "some of ISIS were communists, and that might make you happy."

A convoy of Turkish backed Free Syria Army about to cross into Turkey near the town of Azaz, Syria, on Wednesday. (AP Photo)

"I asked the president what his plan was to contain ISIS," Schumer said. "He didn't really have one. He said the Turks and the Syrians will guard the ISIS prisoners. I said, 'Is there any intelligence evidence that the Turks and Syrians will have the same interest that the Kurds or we did in guarding ISIS?' And the secretary of defense, thank God he was honest, said, 'We don't have that evidence.' So I said, 'How can we think this is a plan?'"

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Schumer added that the situation was "appalling," and that the president was "insulting, particularly to the speaker, but he called her a third-rate politician. He said that there are communists involved, and you guys might like that. This was not a dialogue, this was a diatribe -- a nasty diatribe, not focused on the facts."

Hoyer, D-Md., said the situation was unprecedented.

In this photo taken from the Turkish side of the border between Turkey and Syria, in Ceylanpinar, Sanliurfa province, southeastern Turkey, smoke billowed from fires in Ras al-Ayn, Syria, caused by bombardment by Turkish forces, on Wednesday. (AP Photo/Lefteris Pitarakis)

"We were offended deeply by his treatment of the speaker of the House of Representatives," Hoyer said. "Unfortunately, the meeting deteriorated into a diatribe. ... and very offensive accusations being made by the president of the United States. I have served with six presidents. I have been in many, many, many meetings like this. Never have I seen a president treat so disrespectfully a coequal branch of the government of the United States."

The meeting came amid rapid-fire developments in the Middle East. Trump, earlier this week, authorized sanctions against Turkey, after he had threatened to ruin the country economically if it did anything that he considered "off limits" in his "great and unmatched wisdom."

And Fox Business' Trish Regan exclusively obtained a Wednesday letter from Trump to Turkey's president, urging the two to "work out a good deal!"

Syrian forces on Wednesday night rolled into the strategic border town of Kobani, blocking one path for the Turkish military to establish a "safe zone" free of Syrian Kurdish fighters along the frontier as part of its week-old offensive.

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The seizure of Kobani by forces loyal to Syrian President Bashar al-Assad also pointed to a dramatic shift in northeastern Syria: The town was where the United States military and Kurdish fighters first united to defeat ISIS four years ago and holds powerful symbolism for Syrian Kurds and their ambitions of self-rule.

The convoys of government forces drove into Kobani after dark, a resident said. The resident, who spoke on condition of anonymity for fear of reprisal, was one of the few remaining amid fears of a Turkish attack on the town.

In this photo taken from the Turkish side of the border between Turkey and Syria, in Ceylanpinar, Sanliurfa province, southeastern Turkey, smoke billows from targets in Ras al-Ayn, Syria, during bombardment by Turkish forces, Wednesday, Oct. 16, 2019. Turkey's President Recep Tayyip Erdogan called Wednesday on Syrian Kurdish fighters to leave a designated border area in northeast Syria 'as of tonight' for Turkey to stop its military offensive, defying pressure on him to call a ceasefire and halt its incursion into Syria, now into its eighth day. (AP Photo/Lefteris Pitarakis)

Syria's state-run media confirmed its troops entered the town.

Syria's presence in Kobani puts a firm limit on Turkish ambitions in its offensive. The town lies between a Turkish-controlled enclave farther west and smaller areas to the east that Turkey seized in the past week.

Turkey had talked of creating a 19-mile deep "safe zone," driving out Kurdish fighters from the border region. Turkish forces had shelled Kobani in recent days as part of the offensive but had not advanced ground troops on it.

The battle for Kobani turned the once-nondescript town into a centerpiece of the international campaign against ISIS, with TV cameras flocking to the Turkish side of the border to track the plumes of smoke rising from explosions in the besieged town. Then-U.S. Secretary of State John Kerry declared it would be "morally very difficult" not to help Kobani.

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The ISIS extremists were finally driven out in early 2015 in their first major defeat, and an alliance was cemented that would eventually bring down the group's "caliphate" in Syria.

Now the Kurdish authority agreed to allow Damascus to deploy its military in the town and other parts of northeast Syria to protect them from Turkey's offensive launched after Trump pulled back American troops working with the Kurds.

After being effectively abandoned by the U.S., the Kurds' turn to the Syrian government for protection has allowed Damascus' ally, Russia, to step in as the biggest power player.

Fox News' Chad Pergram and The Associated Press contributed to this report.