Early voting in Ohio the weekend before the election was restored for all voters on Friday by the United States Court of Appeals for the Sixth Circuit, giving President Obama’s campaign another victory in its legal battles with Republicans over voting issues.

The state’s Republican-led administration had imposed a measure that allowed voting that weekend only for members of the military and people living overseas, arguing that the state had to reduce the strain on the election system from statewide early balloting.

Democrats and Mr. Obama’s campaign had cried foul, arguing that the measure unfairly disenfranchised minorities and others who often wait until the last weekend. Those voters are considered likelier to back the Democratic candidates.

Ohio is a critical state in the presidential campaign. No Republican has won the presidency for more than 100 years without winning Ohio. Mr. Obama holds an edge in the state over Mitt Romney in most public polls.

But the decision by the appeals court on Friday was just one of a series of victories for Mr. Obama’s campaign, which has been fighting legal battles in several states over the question of access to the ballot box in the election next month.

In Pennsylvania, a judge this week temporarily blocked a state law that would have required the state’s voters to provide a photo ID card to vote in the presidential election. The state judge accepted the need for such a law but said the state had not done enough to make identification cards easy to get.

This summer, a federal judge blocked a Florida law that would have made it harder for organizations to register people to vote. In that case, the law would have imposed penalties on groups that did not follow specific guidelines and timelines. Advocates said the law was needed to combat voter fraud. Democrats saw it as an effort by the Republican-controlled Legislature to make it harder for Democratic constituencies to vote. Judge Robert Hinkle of Federal District Court blocked the law, calling it “harsh and impractical.”

In Ohio, a district judge blocked the early voting measure in August, saying that the state had a duty to offer equal voting opportunities to all of its residents. On Friday, the appeals court affirmed the judge’s decision.

“Defendants’ legitimate regulatory interests do not outweigh the burden on voters whose right to vote in the upcoming election would be burdened by the joint effect of the statute and the directive,” Judge Eric Clay wrote.

Bob Bauer, the general counsel for Mr. Obama’s campaign, hailed the circuit court’s decision.

“Across the country, the hard work to protect Americans’ right to vote has paid off,” Mr. Bauer said in a statement. “We are now focused on making sure that voters across the country fully understand their rights, know exactly what their voting laws require of them, and clarify when they can cast their ballot.”

Ohio election officials, including Attorney General Mike DeWine, could appeal the ruling.

“My office is reviewing today’s decision by the court as we determine the best course of action moving forward,” said Ohio’s secretary of state, Jon Husted. “No action will be taken today, or this weekend.”