The fast-burning, eight-hour exchange between political rivals came about as an accident of Nevada political scheduling, but it played out far more suggestively — as the most direct confrontation yet between Mr. Trump and one of his leading potential opponents in the 2020 election. And it unfolded on a portentous stage, in the cities and suburbs of a state that is likely to be crucial both in the Democratic presidential primaries and in the general election.

Mr. Trump came to Las Vegas not to needle Ms. Warren, but to raise money for an embattled Republican senator, Dean Heller, seeking re-election in a state where Hillary Clinton beat Mr. Trump in 2016 by a little more than two percentage points. Ms. Warren mapped her own Nevada visit — a swing through Reno and the Las Vegas suburbs — in part to help Mr. Heller’s challenger, Representative Jacky Rosen, and had planned it well before Mr. Trump revealed that he would be in town.

Yet 2020 hung over the day from the outset: Ms. Warren, addressing a convention of the Nevada Democratic Party in Reno, thundered against Mr. Trump’s administration, bringing a crowd to its feet with exhortations to take on corporate special interests and “drive Donald Trump and his enablers out of power.” In a call to elect more women to high office, Ms. Warren tucked in an oratorical wink to the crowd: One of those offices, she said, was “that really nice, oval-shaped room at 1600 Pennsylvania Avenue.”

The current occupant of the Oval Office, sweeping into an event of his own in Las Vegas, could have easily ignored the presence of a combative critic some 400 miles away. But Mr. Trump did not, instead looking away from the ostensible subjects of his visit — Mr. Heller and the tax cuts he helped pass — to swing repeatedly at Ms. Warren.

He labeled her, not for the first time, as “Pocahontas,” a biting reference to Ms. Warren’s description of herself as having Native American ancestry. Mr. Trump and other Republicans have questioned that claim, sometimes drawing criticism from Native American tribes for their mocking language.