President Trump and congressional Democratic leaders ripped off the bandage over their raw, partisan disagreements Tuesday in open bickering that offered a glimpse of the divided government to come in the next two years.

During a White House meeting intended to seek common ground to avoid a partial government shutdown next week, the president and incoming House Speaker Nancy Pelosi and Senate Democratic leader Charles E. Schumer instead squabbled over funding for the border wall, traded blame for the last shutdown and jousted over which party commands the stronger political hand since the midterm elections.

“Unfortunately, this has spiraled downward,” Mrs. Pelosi told the president as their quarreling grew more intense in the Oval Office, which was adorned incongruously with festive holiday decorations.

Most of the feuding played out on camera in front of reporters who were invited by the president to cover the meeting. The Democrats pleaded with Mr. Trump several times to kick out the press.

“Let’s debate in private,” Mr. Schumer urged as cameras continued to roll.

The stormy session ended — at least the public portion of it — with the president declaring he would be “proud” to shut down parts of the government if he doesn’t get more funding for the wall.

“I will take the mantle of shutting down, and I’m going to shut it down for border security,” said Mr. Trump, who uttered the phrase “border security” 29 times in 18 minutes.

The White House later called the meeting “constructive,” although press secretary Sarah Huckabee Sanders acknowledged that “major disagreement remains on the issue of border security and transparency.”

“So far, the Democrat Party has made clear they would rather keep the border open than the government open,” she said. “President Trump was grateful for the opportunity to let the press into the meeting so that the American people can see firsthand that while Republicans are fighting to protect our border, Democrats are fighting to protect illegal immigrants. This administration will always put Americans first.”

Mr. Schumer referred to the president’s behavior as a “temper tantrum.” Mrs. Pelosi later reportedly told colleagues that Mr. Trump’s insistence on the border wall is “a manhood thing.”

The president called Mrs. Pelosi later in the day and discussed a way forward but reached no agreement, her office said.

The meeting was the first for Mr. Trump and the Democratic leaders since Democrats won the House majority Nov. 6 and Republicans bucked the midterm trend by adding two seats to their Senate majority. Expectations were low, with Mr. Trump continuing to call for $5 billion in border-wall funding opposed by Democrats, and Mr. Schumer announcing that any infrastructure legislation next year must include provisions addressing climate change, a certain non-starter with the president.

Adding to the mix were Democrats’ calls in recent days for Mr. Trump to face impeachment or indictment over alleged campaign-finance violations involving hush-money payments to two women who say they had affairs with him.

The hostile relations between Mr. Trump and congressional Democrats are expected to spread far beyond fights over illegal immigration and border security, potentially bringing the president’s legislative agenda to a grinding halt. House committees are ready to start numerous investigations and subpoena administration officials.

The president started off the meeting by opening it to the press, despite the session having been listed as closed on his schedule. He quickly brought up the border wall, joking that it would be “the easiest of all” the challenges facing them.

“What do you think, Chuck? Maybe not?” the president asked, perched on the edge of his wing chair close to Mr. Schumer.

“It’s called ‘funding the government,’ Mr. President,” the New York Democrat replied coolly.

After reciting statistics about the effectiveness of sections of border wall preventing illegal immigration, the president turned to Mrs. Pelosi, who emphasized the need to avoid a government shutdown.

“You should not have a ‘Trump shutdown,’ ” she told the president.

“Did you say ‘Trump‘ “? the president asked.

“A Trump shutdown,” she repeated.

“I was going to call it a ‘Pelosi shutdown,’ ” the president retorted.

Then the gloves came off, as the lawmakers argued with the president over whether he could gain enough votes for the wall in the current Republican-led House, and Mr. Trump saying it was futile because Senate Democrats would block it from receiving the necessary 60 votes.

As the president spoke animatedly about the border wall, the Democratic leaders frequently avoided his gaze. Vice President Mike Pence sat silently in a wing chair next to the president, taking in the arguments.

Mr. Schumer interrupted at one point to tell the president, “The Washington Post today gave you a whole lot of ‘Pinocchios’ because they say you constantly misstate how much of the wall is built and how much is there.” It was a reference to the newspaper’s feature of evaluating the truthfulness of public officials’ statements.

As the feuding went on, Mrs. Pelosi tried to end it.

“Let’s call a halt to this,” she told the president. “We’ve come in here as the first branch of government: Article I, the legislative branch. We’re coming in, in good faith, to negotiate with you about how we can keep the government open.”

When Mrs. Pelosi reminded the president that Democrats had won back the House, Mr. Trump replied, “And we’ve gained in the Senate.”

Mr. Schumer taunted, “When the president brags that he won North Dakota and Indiana, he’s in real trouble.”

“I did,” Mr. Trump said. “We did win North Dakota.”

Mr. Trump also appeared to irritate Mrs. Pelosi by referring to her tenuous, unfinished bid to attract enough Democratic support to be elected House speaker.

“I don’t think we really disagree so much,” the president said. “I also know that, you know, Nancy is in a situation where it’s not easy for her to talk right now, and I fully understand that.”

She bristled at Mr. Trump, “Please don’t characterize the strength that I bring to this meeting as the leader of the House Democrats who just won a big victory.”

The president, who has often opened up meetings to the press that other presidents would not have, seemed to enjoy the Democrats’ discomfort at airing their legislative laundry in front of journalists.

Mrs. Pelosi complained, “This is the most unfortunate thing. We came in here in good faith, and we are entering into this kind of a discussion in the public view.”

“But it’s not bad, Nancy,” Mr. Trump said. “It’s called transparency.”

Turning again to a possible shutdown, Mr. Trump warned Mr. Schumer, “You don’t want to shut down the government, Chuck.”

“Let me just finish,” Mr. Schumer told the president. “Because you can’t get your way.”

Mr. Trump replied, “Because the last time you shut it down, you got killed.”

Despite the bickering in front of TV cameras, Mr. Trump later said the meeting went well after the press left the room.

“Believe it or not I think it was a very friendly meeting,” he told reporters at another White House event. “I’ve actually liked them for a long period of time and I respect them both and we made a lot of progress.”

The president cited progress on a farm bill, and an upcoming Senate vote on a criminal justice reform bill as examples of bipartisan agreement.

“That’s a big thing,” he said.

The president, whose biggest campaign promise in 2016 was building the wall, said he believes he can’t lose on the issue.

“If we have to close down the country over border security, I actually like that in terms of an issue,” he said. “It’s something the country needs. I don’t mind owning that issue. If we close down the country, I will take it. Because we’re closing it down for border security. I think I win that every single time.”

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