Senator Manchin’s announcement that he would not seek re-election is sending shockwaves through the political world as third-party groups seek a candidate, and Democrats look for paths to hold the Senate.

Governor Justice, who is running for Senate as a Republican in West Virginia, said that while the two men have “not always agreed on policy and politics,” “we’re both lifelong West Virginians who love this state beyond belief, and I respect and thank him for his many years of public service.”

The head of the Republican Senatorial Committee, Senator Daines, didn’t mince words on what he thought of Mr. Manchin’s retirement, saying just, “We like our odds in West Virginia.”

A co-chairwoman of the West Virginia Republicans Executive Committee, Elgin McArdle, said in a statement that Mr. Manchin’s retirement “is an important development in ensuring” that Republicans win the seat.

While Mr. Manchin’s announcement signals a near-certain loss for Democrats in the race for the West Virginia Senate seat, Mr. Manchin also indicated that he planned to tour the country to take the temperature of a potential centrist coalition.

“I have made one of the toughest decisions of my life and decided that I will not be running for re-election to the United States Senate, but what I will be doing is traveling the country and speaking out to see if there is an interest in creating a movement to mobilize the middle and bring Americans together.”

Some groups have been explicitly seeking an independent bid for president from Mr. Manchin, such as a draft committee aimed at recruiting Mr. Manchin and Senator Romney to run as a ticket.

The committee filed its paperwork with the Federal Elections Commission Thursday and, according to the Associated Press, is planning to launch its website, America Back on Track, next week.

The committee is aimed at recruiting the two senators to run for the White House on the No Labels ticket, a group that is ostensibly aiming to nominate an independent presidential candidate.

Mr. Manchin is a former honorary co-chairman of No Labels and has been closely associated with the Problem Solvers Caucus, a group with which No Labels is associated closely.

While Mr. Manchin has said he would not seek another office if he didn’t think he would win the election, speculation has run rampant that he might join No Labels as a presidential candidate even though there is likely no path to victory on that ticket.

No Labels, in a statement on Mr. Manchin’s retirement from the Senate, said that the Senate “will lose a great leader when he leaves, but we commend Senator Manchin for stepping up to lead a long overdue national conversation about solving America’s biggest challenges.”

“Regarding our No Labels Unity presidential ticket, we are gathering input from our members across the country to understand the kind of leaders they would like to see in the White House. As we have said from the beginning, we will make a decision by early 2024 about whether we will nominate a Unity presidential ticket and who will be on it,” the group said.