WASHINGTON — President Trump abruptly blew up a scheduled meeting with Democratic congressional leaders on Wednesday, lashing out at Speaker Nancy Pelosi for accusing him of a cover-up and declaring that he could not work with them until they stopped investigating him.

He then marched out into the Rose Garden, where reporters had been gathered, and delivered a statement bristling with anger as he demanded that Democrats “get these phony investigations over with.” He said they could not legislate and investigate at the same time. “We’re going to go down one track at a time,” he said.

The confrontation came on a day when pressure over a possible impeachment effort raised temperatures on both sides of the aisle. Ms. Pelosi arrived at the White House for a session with the president set to talk about infrastructure shortly after meeting with restive House Democrats on Capitol Hill to talk about impeachment. She emerged from that meeting with Democrats accusing Mr. Trump of a “cover-up.”

When she and Senator Chuck Schumer of New York, the Democratic leader, arrived at the White House, Mr. Trump was loaded for bear. He walked into the Cabinet Room and did not shake anyone’s hand or sit in his seat, according to a Democrat informed about the meeting. He said that he wanted to advance legislation on infrastructure, trade and other matters, but that Ms. Pelosi had said something “terrible” by accusing him of a cover-up, according to the Democrat.

After just three minutes, he left the room before anyone else could speak, the Democrat said. From there, he headed to the Rose Garden, where a lectern had been set up with a sign that said “No Collusion, No Obstruction” and gave statistics intended to show that he had cooperated with the special counsel, Robert S. Mueller III.

“Instead of walking in happily into a meeting, I walk in to look at people that have just said that I was doing a cover-up,” Mr. Trump said. “I don’t do cover-ups.”

“I walked into the room and I told Senator Schumer, Speaker Pelosi: ‘I want to do infrastructure. I want to do it more than you want to do it. I’d be really good at that, that’s what I do. But you know what? You can’t do it under these circumstances. So get these phony investigations over with,’” he said.

The Democratic leaders returned to Capitol Hill and expressed disappointment, saying they were ready to make a deal with the president on a $2 trillion plan to rebuild the nation’s roads, bridges, airports and other infrastructure.

“He just took a pass and it just makes me wonder why he did that,” Ms. Pelosi said. “In any event, I pray for the president and I pray for the United States of America.”

Mr. Schumer expressed shock at the outcome. “What happened in the White House would make your jaw drop,” he said.

He suggested that the real reason Mr. Trump blew up the meeting was that he had not come up with a way to pay for such an enormous spending package and therefore was looking for other excuses. He said it did not make sense that investigations would cause such an eruption because they had met late last month to discuss infrastructure.

“Hello! There were investigations going on three weeks ago when we met, and he still met with us,” Mr. Schumer said. “But now, when he was forced to say how he would pay for it, he ran away. And he came up with this preplanned excuse.”

Mr. Trump has been venting his frustration with the continuing investigations with regularity in recent days. In his report, Mr. Mueller established that Russia sought to influence the 2016 presidential campaign to benefit Mr. Trump but that he could not establish any conspiracy or coordination with Mr. Trump’s campaign. Mr. Mueller outlined nearly a dozen instances when Mr. Trump, as president, sought to impede the investigation but offered no conclusion about whether those efforts constituted obstruction of justice.

In his appearance in the Rose Garden, Mr. Trump once again claimed vindication by the report and accused Democrats of refusing to accept that he did nothing wrong. Mr. Trump has vowed to defy all subpoenas for testimony and documents sought by the House, which has angered enough Democrats that pressure is building to open a formal impeachment inquiry.

Mr. Trump emphasized that he and his team provided documents and testimony to Mr. Mueller without citing executive privilege even though he said the special counsel was biased against him, and although he did not himself agree to be interviewed in person.

“These people were out to get us, the Republican Party and President Trump, they were out to get us,” he said, referring to himself in the third person. “So here’s the bottom line,” he added. “There was no collusion, there was no obstruction. We’ve been doing this since I’ve been president, and actually the crime was committed on the other side.”