Updated Senator George V. Voinovich of Ohio announced Monday that he would not seek re-election in 2010.

Mr. Voinovich, whose more than four decades in public life included stints as the governor of Ohio and mayor of Cleveland, said in a statement that his final two years in office would be “the most important years that I have served in my entire political career.”

“I must devote my full time, energy and focus,” he said, “to the job I was elected to do, the job in front of me, which seeking a third term – with the money-raising and campaigning that it would require – would not allow me to do.”

Mr. Voinovich follows three other Republican senators — Christopher S. Bond of Missouri, Mel Martinez of Florida and Sam Brownback of Kansas — who have also said they will not seek another term in two years. Another Republican, Senator Kay Bailey Hutchison of Texas, has signaled that she may cut her term short to run for governor in 2010.

Mr. Voinovich’s retirement will leave another seat vulnerable to poaching by Democrats. Ohio, a critical battleground state in recent presidential elections, voted for Barack Obama in 2008. And in 2006, a Democrat, Sherrod Brown, unseated a Republican incumbent, Mike DeWine, who served two terms in the Senate.

In announcing that he would not seek another term, Mr. Voinovich avoids what could have been a difficult re-election fight. As recently as December a Quinnipiac University poll found that fewer than half of all voters in the state — 44 percent — said he deserved to be elected to a third term. And voters were nearly evenly split on the question of whether they would vote for him or an unnamed Democrat.

Among those who are reportedly angling to replace Mr. Voinovich is a former Ohio congressman, Rob Portman, a Republican who served as director of the Office of Management and Budget and United States Trade Representative during the Bush administration.

Mr. Portman has not yet announced his candidacy, but Matt Miller, a spokesman for the Democratic Senatorial Campaign Committee, sought to pre-empt him on Monday.

“It’s jaw-dropping,” Mr. Miller said, “that Republicans would seem to turn to a Washington insider like Rob Portman who was one of the architects of the Bush economic policies that have run up trillions in deficits and shipped jobs overseas.”

Mr. Voinovich, who will be 74 in 2010, said that although “I still have the fire in my belly to do the work of our nation,” he and his wife, Janet, decided they also wanted to spend more time with their children and grandchildren.

On Monday, Mr. Voinovich also laid out his priorities for the remainder of his term.

“I will continue to focus on the areas that matter most,” he said, “providing the nation a responsible stimulus package; jump-starting our credit markets; re-establishing confidence in the housing market and stemming the tide on mortgage foreclosures; harmonizing our nation’s economic, energy and environmental policies; ensuring safe and stable highways; and continuing to improve the personnel and management of the federal government.”