Matt Dolan, a Republican, Will Challenge Senator Sherrod Brown in Ohio

State Senator Matt Dolan of Ohio, a Republican, announced on Tuesday that he would run for the United States Senate against Sherrod Brown, one of the most vulnerable Democrats in 2024.

It will be Mr. Dolan’s second Senate campaign, after he finished third in the Republican primary for an open seat in Ohio last year. The winner of that primary, J.D. Vance, went on to win the general election.

Mr. Dolan’s family owns the Cleveland Guardians baseball team, and he used millions of dollars of his own money to fund his first campaign, in which he won about 23 percent of the primary vote — finishing significantly behind Mr. Vance and narrowly behind the second-place finisher, Josh Mandel.

In his campaign announcement on Tuesday, Mr. Dolan, the chairman of the Ohio Senate’s finance committee, emphasized border security, fighting inflation and his support for the police. He accused Mr. Brown of “blind loyalty to his party.”

“Ohioans want a problem solver who has successfully faced big challenges impacting our quality of life, not the political blame game that lacks commonsense solutions,” he said. “I have a proven conservative record of success that has yielded results for Ohio families, workers and businesses.”

A tough line on immigration was also a hallmark of Mr. Dolan’s 2022 campaign, though he broke from his opponents’ hard-right line on at least one specific policy: He supported the preservation of H-1B visas that allow immigrants to work temporarily in certain industries.

Mr. Dolan is a former chief assistant prosecutor in Geauga County, east of Cleveland, and a former assistant state attorney general.

Ohio, a former swing state that has moved toward Republicans in recent years, represents one of several opportunities for the G.O.P. to pick up a Senate seat in 2024, with Democratic incumbents in the red states of Montana and West Virginia also up for re-election.

Mr. Brown, a three-term senator and former representative, has won difficult races before, though, including in 2018, when he won re-election by more than six percentage points just two years after Donald J. Trump won in Ohio by eight.

Mr. Brown has shown strong — and enduring, even in the past few years — appeal among the blue-collar voters who are essential in Ohio elections. As chairman of the Senate Banking Committee, he has pushed for more oversight of Wall Street and more consumer protections. He has also been a vocal proponent of expanding the child tax credit and other elements of the social safety net, including the Supplemental Security Income program for disabled and older Americans.

A spokesman for Mr. Brown did not immediately respond to a request for comment on Mr. Dolan’s announcement, but Mr. Brown’s campaign quickly sent a fund-raising email to supporters calling Mr. Dolan “the first of what we expect to be many challengers jumping into the race.”

Among others, Republicans are watching Frank LaRose, the Ohio secretary of state, who has not announced whether he will run but is widely expected to do so.