Mr. Moore’s backers “aren’t the face of the Republican Party that I know,” he added.

Yet with their majority now reduced to a single seat, Senator Mitch McConnell of Kentucky, the majority leader, and his lieutenants remain uneasy about what antiestablishment forces could do in next year’s primary races and have identified at least two additional campaigns where they believe Bannon-backed candidates could weaken the party.

Mr. McConnell’s allies plan to intervene as aggressively as needed in Arizona, where Kelli Ward, a far-right former state legislator, is seeking the seat that will be vacated by Senator Jeff Flake, and in Nevada, where Danny Tarkanian, a perennial candidate who has branded himself as a Trump cheerleader, is challenging Senator Dean Heller in a Republican primary race.

Both candidates, McConnell advisers said, would be completely intolerable as general election nominees.

Complicating matters further for Republicans in Arizona is the health of Senator John McCain, who has an aggressive form of brain cancer and is struggling with the side effects of his treatment. Mr. McCain has made clear he will leave the Senate and return to his home state if he is not able to carry out his duties. But if Arizona’s governor fills the seat by appointing Representative Martha McSally, an all but declared candidate, it could deprive Republicans of perhaps their most formidable candidate against Ms. Ward and further imperil their prospects for retaining the seat held by Mr. Flake, who is retiring.

Establishment-aligned Republicans are still anxious about whether Chris McDaniel, a hard-line Mississippi state senator, plans to challenge Senator Roger Wicker in a primary race next year. Should Mr. McDaniel, who narrowly lost to Senator Thad Cochran in 2014, claim the nomination, it could energize black Mississippians in the same fashion as black Alabamians on Tuesday.

Mr. McDaniel said Wednesday that he was “leaning toward the Senate race,” but he would not rule out the possibility of instead running for lieutenant governor in 2019.