Ben Carson, the only Republican to have once threatened the lead of Donald J. Trump in national polls, said on Wednesday that he saw no path forward and would skip a debate on Thursday in his hometown, Detroit, signaling an end to his candidacy after paltry performances in the nominating contests.

Mr. Carson stopped short of suspending his campaign and said he would provide more details on Friday, but after his dismal showing on Super Tuesday, his campaign is effectively over.

A retired pediatric brain surgeon, Mr. Carson long held Republicans’ favor with an uplifting biography and a quiet manner that belied his strafing critiques of President Obama and liberalism, which delighted grass-roots conservatives.

But in the end, Mr. Carson withered under mocking insults hurled at him by Mr. Trump, especially in Iowa, and he suffered from voters’ desire for a candidate projecting strength at a time of anxiety over terrorism.