The initial count of votes has not yet been completed, as ballots in these populous, Democratic-leaning counties are still being counted.
Election Supervisors have until noon Saturday to turn in what are known as the first unofficial results.
Broward Elections Supervisor Brenda Snipes said she didn't know how many ballots remain to be counted, but all were being processed.
His opponent, Bill Nelson, is also suing the state over uncounted ballots.
"The results are unknown", said Marc Elias, an attorney for Mr Nelson's campaign. "I will not sit idly by while unethical liberals try to steal this election from the people of Florida", Scott added, though he offered no proof to back up his claim.
Judge Carol-Lisa Phillip said Snipes must allow inspections on or before 7:00 p.m. Friday evening. "We are still counting ballots in Broward County".
The information sought includes ballots not yet reviewed by the Canvassing Board, absentee ballots and early voting ballots.
"FDLE is working with the Department of State and we will investigate any allegations of criminal activity or fraud", FDLE spokeswoman Gretl Plessinger told TPM.
Another cluster of House races with votes still being counted could widen the Democrats' new majority, strengthening their hand to counter Trump's policies. Shortly after, President Donald Trump tweeted that law enforcement was looking into another big corruption scandal, claiming "Florida voted for Rick Scott!".
Trump on Friday said Scott "won by a comfortable margin" before suggesting without evidence that Democrats were committing fraud in the election. That's why Governor Rick Scott, who is running to unseat Democratic Sen.
The Associated Press has called the governor's race for DeSantis. "They are asking courts to overrule election officials and accept ballots that were not legally cast". That would be fine if elections supervisor Brenda Snipes were following the laws requiring transparency in the process, but she's not. He said officials performing the count do not have the necessary training to match signatures, and that similar laws in other states have been thrown out.
The former congressman also argued that wider reforms to the election systems should be looked at, such as using blockchain technology, as well as moving Election Day to a weekend to increase the accessibility of voting.
"If you look at Broward County, they have had a awful history", Trump added, referring to a Democrat-heavy county where officials were slowly counting votes including absentee and provisional ballots. He's asked the Florida Department of Law Enforcement to investigate. Those are the U.S. Senate race, Florida Governor's race, and the contest for state Agriculture Commissioner. Bill Nelson, the Democratic incumbent.
November 15: Machine recounts are due by 3 p.m.
"Late Tuesday night, our win was projected to be around 57,000 votes", Scott explained to reporters.
Mr. Gillum had conceded to Mr. DeSantis on Tuesday night. The Nelson-Scott race, as of Friday afternoon, was within 0.18 percentage point, with Scott holding a 14,985 lead with 8.2 million votes counted.
Scott holds a slim lead over Nelson in the race.
The tight races underscored Florida's status as a perennial swing state where elections are often decided by the thinnest of margins.
Scott carried a larger lead Tuesday night, but continues to see it dissipate as more votes come in.