Gov. Brian Kemp of Georgia has decided against running for Senate in 2026, robbing Republicans of their top potential recruit against Senator Jon Ossoff, who is seen as the chamber’s most vulnerable Democrat on the ballot next year.

Mr. Kemp is a popular two-term governor who won re-election in 2022 despite a primary challenge fueled by President Trump, who stewed publicly over Mr. Kemp’s refusal to indulge his false claims that the 2020 election was fraudulent.

Top Republicans had nonetheless sought to woo Mr. Kemp into the Senate race, with Senators John Thune, the majority leader, and Tim Scott, the chairman of the National Republican Senatorial Committee, making a recent visit. Polls had shown he would have been a formidable challenger to Mr. Ossoff, who narrowly won election in 2020.