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

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 simultaneously. “We’re going to go down one track at a time,” he said.

The tempestuous clash between Mr. Trump and Ms. Pelosi suggested that efforts to forge bipartisan legislation on issues — already a long shot — may effectively be frozen for the foreseeable future while the president and his opponents wage war over the various investigations now underway.

The confrontation came on a day when talk of a possible impeachment drive raised temperatures on both sides of the aisle. Restive House Democrats pressed Ms. Pelosi to open a formal inquiry aimed at removing the president from office for high crimes and misdemeanors while both sides sought to gain the upper hand in the escalating conflicts over testimony and documents.