The chairman of the Republican National Committee, Michael Whatley, plans to run for the Senate in North Carolina with the backing of President Trump, after Lara Trump, the president’s daughter-in-law, declined to run herself, according to two people with knowledge of the decision.

The election to fill the North Carolina seat, which is opening up with the retirement of Senator Thom Tillis, a Republican, at the end of his term, is expected to be one of the most expensive and contested races of 2026.

Democrats have recruited the popular former two-term Gov. Roy Cooper, who is planning to enter the race as early as next week.

Mr. Trump has taken a direct interest in a number of Senate contests to be held next year, including in North Carolina. With Mr. Whatley’s entrance, and with Mr. Trump expected to endorse him, Republicans hope to avoid a long and costly primary and can begin to focus on Mr. Cooper, one of the people said.