Former Vice President Joseph R. Biden Jr. conjured the prospect of headlines like, “Look what happens when the Labour Party moves so, so far to the left.” Former Mayor Michael R. Bloomberg said that “Jeremy Corbyn’s catastrophic showing in the U.K. is a clear warning.” And Mayor Pete Buttigieg spoke of the need to “build a coalition and gather that majority.”

As Britain’s Labour Party grappled on Friday with its worst performance in more than 80 years, centrist Democrats across the Atlantic seized on those election results — with varying degrees of urgency — to argue that their own party risked losing in November by moving too far to the left. The day-after assessments threatened to deepen the tensions between moderates and progressives that have shaped the 2020 presidential campaign from the start.

The comparisons between the Labour Party and the Democratic Party, and between the candidates representing them, are far from perfect, and make it difficult to draw precise parallels to American political dynamics. The British election was focused in significant part on the issue of leaving the European Union, as Prime Minister Boris Johnson pressed to “get Brexit done” and convinced a solid majority of voters that he was on the right path. Mr. Corbyn faced controversies at home, including a crisis in his party over accusations of anti-Semitism.

But moderate presidential candidates, strategists and other party leaders in the United States said Friday that the results in Britain offered ominous signs about nominating a candidate perceived as out of the political mainstream.