TALLAHASSEE — U.S. District Judge Mark Walker on Thursday granted an injunction giving voters until 5 p.m. Saturday to fix mail and provisional ballots that were rejected because of mismatched signatures.

The order applies to voters who were "belatedly notified" that they had a signature problem. Walker called it "a limited order providing limited relief for a limited number of affected voters."

UPDATE: Gov. Rick Scott's Senate campaign called the decision "baseless" and filed an appeal with the 11th Circuit Court of Appeals in Atlanta. Democratic lawyers filed an emergency motion with Walker that asks the judge to order the state to provide the names of every Florida voter affected by the decision. That motion is expected to be heard at 2 p.m. Thursday.

Walker issued a 34-page order at 1:15 a.m. on Thursday that said Florida's "questionable practice" for curing ballot signature mismatches has "no standards, an illusory process to cure and no process to challenge the rejection," and as a result does not pass constitutional muster.

"Florida law provides no opportunity for voters to challenge the determination of the canvassing board that their votes do not count," Walker wrote. "Interestingly, Florida law does provide an opportunity for any voter or candidate to challenge a signature that was accepted and thus a vote that was counted."

Read the judge's order here.

"Let this court be clear," Walker wrote. "It is NOT ordering county canvassing boards to count every mismatched vote, sight unseen. Rather, the county supervisors of elections are directed to allow those voters who should have had an opportunity to cure their ballots in the first place to cure their vote-by-mail and provisional ballots now, before the second official results are fully counted."

Information presented during a five-hour court hearing Wednesday showed that 45 of the state's 67 counties have rejected 3,688 mail ballots and 93 provisional ballots because of signature mismatches. Two of the state's largest counties, Miami-Dade and Duval, did not report numbers.

Democratic Sen. Bill Nelson unofficially trails Scott in the Senate race by 12,562 votes, or 0.15 percent.

Scott's administration and the National Republican Senatorial Committee argued against an injunction, and asserted that the lawsuit by Senate candidate Nelson and the Democratic Executive Committee of Florida was barred because it wasn't filed before election day.

In announcing an appeal, Scott's campaign said Nelson's attorneys are making the opposite argument on signature mismatches in Arizona, in a case where the Democratic candidate was leading and the Republican was trailing.

"What this case comes down to," Walker wrote, "is that without procedural safeguards, the use of signature matching is not reasonable and may lead to unconstitutional disenfranchisement."

Walker ordered Secretary of State Ken Detzner to issue a directive to all 67 supervisors of elections, with the court order attached, telling them that Florida's cure for signature mismatches has been applied unconstitutionally and that they are required to allow voters who were belatedly notified of a mismatch that they have until 5 p.m. Saturday to correct any mistakes.

The new deadline is 22 hours before all counties must report their final election returns to the state, including manual recount results.

Walker's order places additional pressure on Democrats, and Nelson's Senate campaign, to find as many of those excluded voters as soon as possible to seek to have their votes count.

Walker also denied all of the defendants' request for a stay pending appeal.

It's unclear if Walker's order will affect Thursday's 3 p.m. deadline for supervisors of elections to turn in the results from their state-mandated recounts of the U.S. Senate race between Nelson and Scott, the governor's race, commissioner of agriculture's race and any other down-ballots contests that required a recount.

Neither is it yet clear exactly how many ballots were rejected over mismatched signatures, since the state had totals from only 45 of Florida's 67. Because of his 12,500 vote deficit, Nelson almost certainly won't be able to make up that difference based on ballots made valid through Walker's ruling.

Walker, however, is set to hear lawsuits challenging the state's process for counting overvotes and undervotes and seeking to extend the deadline for supervisors of elections to submit their recount totals. Nelson's campaign is also hoping to make up ground through the counting of thousands of overvotes and undervotes.