Ohio Republicans have backed down on an effort to penalize the state’s largest county for sending out absentee ballots. But the escalating battle over voting rights in the nation’s most pivotal swing state shows no sign of subsiding—with one top Democrat calling for a federal probe of GOP voter suppression.

A spokesman for House Republicans said Tuesday afternoon that the GOP would drop a measure that would have cut funding by 10% for any county that doesn’t follow state law regarding absentee ballots. The proposal, inserted Monday into a larger budget bill, was a direct shot at the state’s largest county, Cuyahoga, which has asserted the right to mail absentee ballots to all registered voters—in defiance of a recently passed state law barring counties from doing so.

Hours later, the Cuyahoga council voted to assert its “home rule” power, giving it the authority to send absentee ballots to all registered voters in the county.

The GOP’s decision to pull the funding measure reportedly came after Gov. John Kasich, a Republican, asked House members to do so. But Cuyahoga County Executive Ed FitzGerald, a Democrat who is challenging Kasich this fall, told msnbc he thinks it also was prompted by a letter FitzGerald sent earlier Tuesday, and promoted at a press conference, requesting a federal investigation into the recent wave of restrictive voting rules imposed by Ohio Republicans.

“They were defending it all day yesterday,” FitzGerald said of the Republicans’ funding measure. “They stopped defending it after we had our press conference in front of federal court this morning. I don’t think those things are unrelated.”

In late February, the GOP-controlled state legislature cut early voting, ended same-day registration, and made it easier to reject provisional ballots. Days later, Ohio Secretary of State Jon Husted announced further cuts to early voting, including the elimination of Sunday voting, which has been especially popular with African-Americans.

The absentee ballot law was also part of that wave. Citing the need for uniformity across the state, Republicans passed a bill saying only the secretary of state could mail absentee ballots, and then only with approval from lawmakers.

In 2012, 1.2 million Ohioans voted absentee after Husted mailed absentee ballots to all registered voters. But he did so only as part of an agreement with FitzGerald, who sued after Husted barred counties from mailing absentee ballots on their own.

For his part, Husted suggested in an interview with the Cleveland Plain Dealer Tuesday that the debate over absentee ballots may be moot, because he’s once again planning to mail absentee ballots to every registered voter. Doing so won’t violate the state law because Husted’s office already has the funds for the mailing this year.

FitzGerald said in the council meeting Tuesday afternoon that the county planned to mail absentee ballots only if the state doesn’t. But he told msnbc he doesn’t trust Husted to mail absentee ballots in future years—citing the 2011 absentee ballot dispute, and a 2012 effort by Husted to cut early voting that was stopped by the courts.

“Excuse me if I’m not gonna trust them to continue to do this,” FitzGerald said. “They tried in 2011 and 2012 to restrict voting. Why would I trust them to not try to restrict it in 2016?”

Over one third of Cuyahoga residents are black or Hispanic. In 2012, the county, which includes the city of Cleveland, accounted for about 16% of all votes for President Obama in the state.

The effort to push back against Ohio’s new voting restrictions hasn’t been limited to Cuyahoga. The state Democratic party is mulling a legal challenge to the early voting cuts. African-American leaders are working to get a “Voters Bill of Rights” on the ballot this fall. And national Democrats are lending key backing to state Sen. Nina Turner, a voting rights champion, as she runs for secretary of state against Husted this fall.