TALLAHASSEE — Florida’s historic recount in three statewide elections continued Wednesday with a flurry of courtroom activity that could influence the proceedings, even as local election officials scrambled to meet the Thursday deadline to complete their work.

Election officials in Broward County, a populous Democratic stronghold, said that they would meet the 3 p.m. Thursday deadline for completing a machine recount. Officials in Palm Beach County faced problems with the counting machines themselves and have said they can’t guarantee they’ll be done Thursday.

Representatives of both parties attended a “walk-through” at the Broward elections office to prepare for the manual recount expected to follow in the very tight Senate race, in which Sen. Bill Nelson (D) trails Gov. Rick Scott (R) by fewer than 13,000 votes out of more than 8 million cast.

A state judge in Hillsborough County ruled in Scott’s favor to allow his campaign’s monitors into the room where the recount is taking place. And Nelson’s campaign, along with state Democrats, filed a new lawsuit requesting to inspect records in Bay County, where the election supervisor has said that in the aftermath of Hurricane Michael, he let voters submit ballots electronically, an apparent violation of state law.

Both campaigns were awaiting a court decision on Nelson’s request to count absentee and provisional ballots that were not tallied because voters’ signatures did not match their voter registration records. A five-hour hearing wrapped up Wednesday without an immediate decision.

And more courtroom drama was coming Thursday: Hearings were scheduled in state court in Broward County in two lawsuits that Republicans filed against Broward elections supervisor Brenda Snipes, one of them over 25 ballots that were counted after the first unofficial returns were reported to the state.

Republicans ramped up their accusations of voter fraud against Democrats after the Department of State, which oversees elections in Florida, asked state law enforcement officials and federal prosecutors to investigate allegations that state Democrats sent incorrect voting instructions to mail-in voters in four counties.

The complaint includes examples of four voters who mailed in absentee ballots that lacked sufficient information and were sent follow-up affidavits. Instructions for completing the affidavits said the deadline was last Thursday, two days after the election; the actual deadline was last Monday, the day before the election.

At least three of the four voters affected were Democrats, according to their local election offices, so it’s unclear why someone at the state Democratic Party would give them the wrong deadline or who altered the form.

It is also unclear how many voters received incorrect instructions or how many ballots went uncounted as a result. The Florida Democratic Party did not respond to a request for comment. But Republicans pounced, alleging that Democrats had intentionally encouraged voters to cast or fix ballots after Election Day in the hopes of persuading judges to count those votes.

“After all, an influx of Democratic voters trying to cast their ballots after the deadline could make it easier for Democrats and liberal groups to play games with the legal process and ultimately fight to change the law — just like they are doing right now,” read an email distributed by the Scott campaign Wednesday.

The request appears to be the first time the department has flagged allegations of voting irregularities this year. The department has declined to call for an investigation in Bay County, a predominantly Republican part of Florida; Scott has also declined to weigh in on the situation.

The Senate race will determine the size of the GOP’s majority in 2019 and shape the power structure in the nation’s largest swing state. Together, the two sides have racked up at least 10 lawsuits trying to gain a legal advantage in the recount.

U.S. District Judge Mark Walker presided over a tense hearing Wednesday in a Tallahassee courthouse but recessed without announcing a decision. Reporters and campaign officials packed three rows of seats inside the courtroom, while cameras were staked out in the rain.

Walker seemed open to the possibility of allowing a new and limited window for voters to “cure” their rejected ballots. He reminded lawyers of how important even a limited number of votes could be.

“Do we just dismiss 500 votes? Because last time I checked, 500 votes determined the leader of the free world,” Walker said, making a reference to the Florida recount in 2000 that led to the election of George W. Bush.

Republican attorneys argued that ruling in a way that would allow the counting of some ballots that were disqualified over signature mismatch would amount to a major disruption to a vote-tallying operation that has already been stretched to its limits.

There are nearly 3,700 vote-by-mail ballots that were set aside because of signature mismatch across 45 counties, according to a partial tally from state officials presented by one of the GOP attorneys. The count does not include 22 counties.

Both candidates, meanwhile, were in Washington on Wednesday. At a photo opportunity for new Republican senators, Scott declined to answer questions about whether he still thinks the vote count in Florida has been tainted by fraud.

Scott recused himself from a state commission that certifies the election results, as he did in 2014, when he ran for reelection. But the move is unlikely to satisfy Democrats, who have demanded that he remove himself from any decision-making in the state’s administration of elections.

Although Scott has been a vocal critic of Democrats during the recount, Republican gubernatorial nominee Ron DeSantis has been much quieter. DeSantis, a close ally of President Trump, has a more comfortable margin over Tallahassee Mayor Andrew Gillum (D). Democrats and Republicans are not anticipating a hand recount in the governor’s race. Votes also are being recounted in the race for state agriculture commissioner.

Reinhard reported from Lauderhill, Fla., and Gardner reported from Fort Lauderdale, Fla. Seung Min Kim in Washington contributed to this report.