TALLAHASSEE, Fla. (AP) — A hand recount began Friday in Florida's acrimonious U.S. Senate contest after an initial review by ballot-counting machines showed Republican Gov. Rick Scott and Democratic Sen. Bill Nelson separated by fewer than 13,000 votes out of more than 8 million cast.

Under state law, a hand review is required when the victory margin is 0.25 percentage points or less. A state website's unofficial results show Scott ahead of Nelson by 0.15 percentage points.

The hand recount in the Senate race does not review all votes that were cast. It involves only that fraction of ballots in which voters cast either two votes for one race, which is called an overvote, or appeared to choose no candidate, which is an undervote. The idea is to figure out a voter's intent.

At a warehouse in Broward County — which has had numerous problems throughout the election — dozens of volunteers sitting at folding tables cheered loudly when they were told they had finished the recount Friday morning and could go home for the day. Results were not immediately announced.

The margin in the governor's race between Republican Ron DeSantis and Democrat Andrew Gillum was 0.41 percent. That means the contest for governor appeared all but over Thursday, with a machine recount showing DeSantis with a large enough advantage over Gillum to avoid a hand recount in that race.

Gillum, who conceded on election night only to retract his concession later, said in a statement that "it is not over until every legally casted vote is counted."

The overall recount has been fraught with problems. One large Democratic stronghold in South Florida could not finish its machine recount by the Thursday deadline because of machines breaking down. A federal judge rejected a request to extend the recount deadline.

"We gave a heroic effort," said Palm Beach Supervisor of Elections Susan Bucher. If the county had three or four more hours, it would have made the deadline to recount ballots in the Senate race, she said.

Meanwhile, election officials in another urban county in the Tampa Bay area decided against turning in the results of their machine recount, which came up with 846 fewer votes than originally counted.

Broward County missed the deadline to submit its machine recount results by two minutes, but it finished its manual recount in just a few hours Friday morning, which Elections Supervisor Brenda Snipes attributed to the large number of volunteers assembled for the task.

Scott called on Nelson to end the recount battle.

It's time for Nelson "to respect the will of the voters and graciously bring this process to an end rather than proceed with yet another count of the votes — which will yield the same result and bring more embarrassment to the state that we both love and have served," the governor's statement said.

The margin between Scott and Nelson had not changed much in the last few days, conceded Marc Elias, an attorney working for Nelson's campaign. But he said he expects it to shrink due to the hand recount and the ruling on signatures.

Three election-related lawsuits are pending in federal court in Tallahassee.

The situation drew the ire of U.S. District Judge Mark Walker, who slammed the state for repeatedly failing to anticipate election problems. He also said the state law on recounts appears to violate the U.S. Supreme Court ruling that decided the presidency in 2000.

"We have been the laughingstock of the world, election after election, and we chose not to fix this," Walker said at a hearing Thursday.

Incoming Florida Senate President Bill Galvano said Friday that lawmakers will discuss changes to the state's election laws.

By the next election cycle, he said, "voters are going to want to have more in terms of assurance that their votes are going to be properly counted."

Late Thursday, Walker rejected a challenge by Nelson and Democrats to the rules of the hand recount in the Senate race. During the hand recount, elections officials look at just the ballots that weren't recorded by voting machines. Walker found the state's rules were reasonable and constitutional.

Walker also ordered that voters be given until 5 p.m. Saturday to show a valid identification and fix their ballots if they haven't been counted due to mismatched signatures. Republicans challenged this order and were turned down by an appeals court.

State officials testified that nearly 4,000 mail-in ballots were set aside because local officials decided the signatures on the envelopes did not match the signatures on file. If those voters can prove their identity, their votes will now be counted and included in final official returns due from each county by noon Sunday.

Walker was asked by Democrats to require local officials to provide a list of people whose ballots were rejected. But the judge refused the request as "inappropriate."

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Associated Press writers Tamara Lush in St. Petersburg, Curt Anderson and Kelli Kennedy in Fort Lauderdale and Jennifer Kay in Miami contributed to this report.