US President Donald Trump has abruptly cut short a White House meeting with Democrats on infrastructure, then ripped into them over House Speaker Nancy Pelosi's accusation that he is engaged in a cover-up and asserted that he could not work with them unless they dropped multiple investigations.

"I don't do cover-ups," the Republican president, clearly agitated, told reporters at a previously unscheduled Rose Garden appearance after his brief meeting with Democratic congressional leaders that Ms Pelosi described as "very, very, very strange."

Unleashing a familiar litany of gripes about Special Counsel Robert Mueller's Russia probe and the follow-up congressional inquiries that he has been stonewalling, Mr Trump also complained that Democrats had met to discuss whether to impeach him - or, as he called it, "the I-word."

The rupture bodes ill for any possible cooperation between the president and the Democrats who control the House of Representatives on legislation on infrastructure or other matters as Mr Trump seeks re-election in 2020, signaling deepening political gridlock in Washington.

Ms Pelosi, the top congressional Democrat, did not back down afterward and pointedly mentioned the possibility of impeachment, the US Constitution's process for the House and Senate to remove a president from office.

"The fact is, in plain sight in the public domain, this president is obstructing justice and he's engaged in a cover-up- and that could be an impeachable offense," Ms Pelosi said in an event at the Centre for American Progress, a liberal Washington policy advocacy group.

The president is stonewalling congressional investigations by ignoring subpoenas, refusing to let current and former advisers testify and not handing over documents in the aftermath of the April release of Mr Mueller's report that detailed Russian interference in the 2016 election to boost Mr Trump's candidacy.

After the blow-up of the meeting and Mr Trump's diatribe, Democrats accused him of setting them up and expressed concern about his conduct and the long-term outlook.

"The president has made it clear he doesn't want to consider any substantive issue as long as he's under investigation," Dick Durbin, the No. 2 Senate Democrat, said.

"I've got news for the president: Every president is under investigation. That's the nature of our Constitution," he said.

In the run-up to the infrastructure meeting, Mr Trump was stewing over Ms Pelosi's cover-up remarks, according to a White House official.

Ms Pelosi, amid growing talk about impeachment, had told reporters about an hour before the scheduled meeting that the president was engaged in a cover-up.

As the meeting neared, Mr Trump told aides he wanted to hold an event in the Rose Garden to make a statement.

When Ms Pelosi and Senate Democratic Leader Chuck Schumer arrived in the Cabinet Room, Mr Trump walked in and told them he had asked them over to talk about infrastructure, but that the speaker had just accused him of a cover-up.

The meeting lasted only three to five minutes, the official said.

Afterward, Mr Trump strode to a podium adorned with a professionally made sign that read, "No Collusion, No Obstruction" and that also listed the cost, length and other accusations about the Mueller probe.

Mr Trump said, "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."

Just three weeks ago, Mr Trump and the Democrats agreed to spend $2 trillion on roads, bridges and other infrastructure. The meeting was supposed to be about ironing out the thorny details of how to pay for it all.

"For some reason," Ms Pelosi told reporters, "and maybe it was lack of confidence on his part - that he really couldn't match the greatness of the challenge that we have - he wasn't really respectful of the Congress and the White House working together."

"In any event, I pray for the president of the United States and I pray for the United States of America," Ms Pelosi added.

Mr Trump and the Democrats have become locked in a high-stakes power struggle over the ability of Congress to investigate him, with the president increasingly asserting that his advisers need not respond to lawmakers' requests.

Numerous congressional probes now underway range from whether Mr Trump tried to obstruct Mueller's inquiry to the president's undisclosed tax returns, his handling of numerous policy issues and possible conflicts of interest involving the businesses he has not divested even while serving.

Most of his fellow Republicans dismiss the investigations as political assaults ahead of the 2020 election.