Senator Thom Tillis, Republican of North Carolina, announced on Sunday that he would not seek re-election next year, a day after President Trump threatened to back a primary challenger against him because Mr. Tillis said he opposed the bill carrying Mr. Trump’s domestic agenda.

Mr. Tillis’s departure will set off a highly competitive race in North Carolina that could be pivotal in the battle for control of the Senate. It was the latest congressional retirement to underscore the rightward shift of the G.O.P. and the reality that there is little room for any Republican to break with Mr. Trump.

“In Washington over the last few years, it’s become increasingly evident that leaders who are willing to embrace bipartisanship, compromise, and demonstrate independent thinking are becoming an endangered species,” Mr. Tillis said in a lengthy statement on his decision.

The announcement came as the Senate was wading into a debate over the large-scale tax cut and domestic policy bill that Mr. Trump has demanded be delivered to his desk by July 4. Mr. Tillis announced his decision the day after issuing a statement saying he could not in good conscience support the measure, which he said would lead to tens of billions of dollars in lost funding for his state, costing people Medicaid coverage and critical health services.

Mr. Tillis, 64, is serving his second term, and has been struggling with how to balance a potential re-election campaign with his desire, at times, to oppose Mr. Trump’s agenda.

In his statement, he said he was looking forward “to having the pure freedom to call the balls and strikes as I see fit and representing the great people of North Carolina to the best of my ability” in his remaining time in Congress.