Donald J. Trump won sweeping victories across the South and in New England on Tuesday, a show of strength in the Republican primary campaign that underscored the breadth of his appeal and helped him begin to amass a wide delegate advantage despite growing resistance to his candidacy among party leaders.

Mr. Trump’s political coalition — with his lopsided victories in Alabama, Georgia, Massachusetts and Tennessee, and narrower ones in Arkansas, Vermont and Virginia — appears to have transcended the regional and ideological divisions that have shaped the Republican Party in recent years.

With strong support from low-income white voters, especially those without college degrees, he dominated in moderate, secular-leaning Massachusetts just as easily as he did in the conservative and heavily evangelical Deep South.

Brandishing his Super Tuesday victories as proof of his political might, Mr. Trump said he expected to consolidate the Republican Party behind his campaign.