COLUMBUS (AP) — Two of Ohio’s most prominent Democrats said Tuesday they will run in 2010 for the U.S. Senate seat being vacated by Republican Sen. George Voinovich.

Secretary of State Jennifer Brunner, who largely beat back Republican legal challenges over the way she oversaw the presidential election in November, announced her run for the Senate seat on a campaign Web site.

Lt. Gov. Lee Fisher, who was elected in 2006, held a news conference later Tuesday with Gov. Ted Strickland, apparently pushing up his public announcement in response to Brunner’s decision. Fisher resigned Tuesday from his position as director of the Ohio Department of Development, but will serve out the remainder of his term as lieutenant governor.

The campaigns set up what is likely to be a hard-fought Democrat primary between Brunner, who has built name recognition while overseeing Ohio’s elections, and Fisher, a veteran politician who has run for statewide office multiple times. It also places the crucial secretary of state seat up for grabs for both parties and begins speculation over who will be Strickland’s running mate in 2010 when he is expected to seek re-election.

Brunner said she and Fisher have spoken about avoiding a nasty primary fight. She said her campaign will build on her success as secretary of state, which includes protecting voting rights.

‘‘Looking at where we stand with the economy in this country, it’s even more important to protect jobs in the state of Ohio … I want to be a part of the solution,’’ Brunner said in an interview with The Associated Press.

Fisher had established an exploratory committee after Voinovich announced in January that he would not seek re-election.

Fisher said Barack Obama’s election as president, the failure of Congress to aid the auto industry, and watching the federal economic stimulus package barely survive in the Senate helped clinch his decision.

‘‘We owe it to ourselves to make sure that we have partners in Washington, D.C., who get it, who have spent some time at kitchen tables, who have spent some time in factory lines, who have spent some time in small businesses, who understand,’’ Fisher said. ‘‘Who get out of that thin air of Washington, D.C., and are on Main Street as opposed to Pennsylvania Avenue or Wall Street. So that’s why I’m running.’’