The early voting window, which begins Tuesday, became a partisan battle in this swing state where President Bush narrowly clinched re-election in 2004.
The court decisions were a victory for Ohio Secretary of State Jennifer Brunner, a Democrat who was criticized by Republicans for telling county election boards to allow same-day registration and voting through Oct. 6.
"This ruling is a victory for all Ohio voters," Brunner said in a statement. "It should send a message to the forces of confusion and chaos that our top goal must be protecting Ohioans' voting rights."
The Ohio Republican Party didn't say if it would appeal.
The state GOP and some Republican voters had argued in separate lawsuits that Ohio law requires voters to be registered for 30 days before they cast an absentee ballot.
But in Cleveland, U.S. District Judge James Gwin, an appointee of former President Bill Clinton, rejected that argument Monday and issued a temporary restraining order forcing Madison County to follow Brunner's instructions.
Then in a statewide case, the Ohio Supreme Court by a 4-3 vote said Brunner was correct. The normally all-Republican Ohio Supreme Court had six Republicans and one Democrat for Monday's decision, because two Republican justices recused themselves and Chief Justice Thomas Moyer replaced one with a Democrat, who sided with Brunner.
Finally in Columbus, U.S. District Judge George Smith, an appointee of former President Ronald Reagan, declined to rule on another statewide challenge, deferring to the state Supreme Court's decision. But Smith did rule that party poll observers must be allowed during early voting in the state's 88 counties. Brunner appealed that decision to a federal court in Cincinnati.
Democratic presidential candidate Barack Obama's campaign has urged supporters in Ohio to use the early voting window. Despite the Ohio Republican Party's lawsuits, the Republican National Committee's Web site encouraged Ohio Republicans to use early voting,
Early voting advocates are targeting college students, the homeless, the poor and minoritiesvoters who have traditionally had a hard time getting to the polls.
Obama's campaign planned to organize carpools from college campuses around the state to local polling places. And the Northeast Ohio Coalition for the Homeless hoped to transport 2,000 homeless individuals from shelters to polling places in the Cleveland area.
"This is a win for Jennifer Brunner's partisan efforts to aide the Democrat turnout strategy," Ohio GOP Chairman Bob Bennett said in a statement. "Naturally we're disappointed in these rulings." He didn't address a possible appeal.
Some charged the Ohio Republican Party was trying to suppress the vote.
"There are some forces in the Republican Party that seem bound and determined to suppress the vote by any means necessary," said Dan Tokaji, an Ohio State University elections law expert.
"The Republicans' cynical 11th-hour ploy to disenfranchise Ohio voters has been soundly rejected in federal court," Ohio Democratic Party Chairman Chris Redfern said.
The disputed voting window results from an overlap between Tuesday's beginning of absentee voting 35 days before Election Day, and the Oct. 6 end of voter registration.
Republicans argued that providing an absentee ballot to a voter before verifying the registration could open the door to voter fraud. Brunner instructed election officials to segregate those ballots and verify the registration before they are counted.
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Associated Press Writer Thomas J. Sheeran in Cleveland contributed to this report.