A legal fight deepened over the outcome of Florida’s U.S. Senate race as local election officials raced to meet a Saturday deadline to report voting tallies that are expected to trigger a recount.
Preliminary results since Tuesday show Republican Gov. Rick Scott unseating three-term Democratic Sen. Bill Nelson. But the race has tightened, as election officials count more votes, to show Mr. Scott leading by just over 15,000 votes, or 0.18 percentage point, down from roughly 56,700 on election night.
That narrowing gap has evoked the heated 2000 Florida presidential recount and spurred charges of wrongdoing by the Scott camp and GOP allies, including President Trump. Successful lawsuits by Mr. Scott forced officials in two populous, Democratic-leaning counties to release more information about remaining uncounted ballots. Mr. Nelson, in his own suit, maintained that state election officials could short-circuit the vote-counting process in the nation’s largest battleground state.
Mr. Nelson’s campaign initially appeared to concede but has since called for a recount, brought in top election lawyers and issued nationwide fundraising appeals. Florida law requires a machine recount if the margin is a half percentage point or less, and a hand recount if the spread shrinks to a quarter percentage point, which appeared to be the case.
The Florida governor’s race was also on the verge of a recount because of a similarly close margin, despite initially appearing to go to Republican Ron DeSantis over Democrat Andrew Gillum.
A third Florida race, for the state agriculture commissioner, is also close and will be subject to recount.
The acrimony added to a midterm-election cycle marked by partisan rancor and comes as other key elections were being fought in Arizona, where a Democrat held a nominal lead in the U.S. Senate race, and Georgia, where a Republican is ahead in the governor’s race. Several House races in California remain unresolved.
Mr. Scott’s lawsuits targeted the two South Florida counties because of what his campaign said were lack of transparency in how many votes were being tallied. Florida Circuit Judge Krista Marx ruled that Palm Beach County Elections Supervisor Susan Bucher had to turn over outstanding ballots to county canvassers by Saturday morning, and Broward County Judge Carol-Lisa Phillips ordered county Elections Supervisor Brenda Snipes to release the number of votes cast in the county by Friday evening.
Ms. Snipes and her election office have come under legal scrutiny in the past. A judge ruled this year that she violated law by destroying ballots from a 2016 Democratic congressional primary that came under dispute. Ms. Snipes called that a mistake. Efforts to reach Ms. Snipes for comment were unsuccessful. She has said the count took long because of Broward’s large number of ballots.
The counties face a deadline of noon Saturday to report unofficial results to the state. A recount would commence after that, if the vote tally holds.
Mr. Trump, on his way to Paris for meetings on Friday, addressed the Florida contest repeatedly, asserting without evidence that Democrats were trying to manufacture votes. “I am sending much better lawyers to expose the FRAUD!” he wrote on Twitter.
Mr. Scott echoed that sentiment Friday, even though any votes being counted across the state would presumably add to his vote total in addition to his opponent’s. “The goal is to keep mysteriously finding votes until the election turns out the way they want,” Mr. Scott said.
The governor on Thursday called on the Florida Department of Law Enforcement to conduct a criminal investigation into possible wrongdoing, but a spokesman with the agency said Friday that it hadn’t received any criminal allegations and wasn’t conducting an investigation.
Marc Elias, a top Democratic election lawyer hired by Mr. Nelson’s campaign, said he is confident the Senate margin would continue to narrow. Election officials often take several days to fully tabulate results, and overseas ballots continue to trickle in and will be counted until 10 days after Election Day.
“We believe that when every legal ballot is counted, we will win this election,” Mr. Nelson said in a statement Friday.
Any recount process could take more than a week. Election officials will have until Nov. 15 to complete a machine recount and until Nov. 18 to complete a manual recount, if necessary.
In a federal court filing Thursday, the Nelson campaign and the Florida Democratic Party argued that a signature-matching process for deciding whether to count mail-in and provisional ballots is unconstitutional.
They called for the court to enter a temporary injunction preventing Florida Secretary of State Ken Detzner, a Republican, from “rejecting vote by mail and provisional ballots on the basis of a signature mismatch.” Democrats said that tens of thousands of voters could be disenfranchised under the current system.
Mr. Scott’s campaign blasted that move, saying it amounted to asking “the federal courts to allow voter fraud” and seek to “accept ballots that were not legally cast.”
Besides the Arizona Senate race, two other statewide contests remained too close to call on Friday. A Democrat holds a narrow lead in the race for state schools superintendent, and Republican Steve Gaynor is slightly ahead against a Democratic challenger for secretary of state.
Meanwhile, five California House races are undecided—Democrats lead in two, Republicans in three—with millions of ballots left to be counted statewide. California often counts votes several days after Election Day because the state counts mailed-in ballots as long as they are postmarked by Election Day. Eight races in other states haven’t yet been called.
—Arian Campo-Flores and Reid J. Epstein contributed to this article.