The gap between Mr Scott - the outgoing governor of Florida - and incumbent Democratic Senator Nelson has narrowed to 0.2% as of Friday as Broward County votes are counted.
Razor-thin margins in Florida's bitter races for the U.S. Senate and governor are raising the possibility of recounts, potentially prolonging two of the most closely watched contests of the nation's midterm elections.
Meanwhile, Nelson's reelection campaign has filed a lawsuit against Florida Secretary of State Ken Detzner over vote-by-mail ballots.
The deadline for all 67 Florida counties to submit their first set of unofficial returns is Saturday at noon ET, according to the secretary of state's office.
Every vote that was legally and verifiably cast prior to the polls closing at 7 p.m. on Tuesday should of course be counted.
In his statement, Nelson said he believes once all the ballots are counted, he will win the race.
"If you look at Broward and Palm Beach [counties] to a lesser extent ... they have had a awful history", the president told reporters outside the White House before hopping on a plane for his trip to Paris.
Earlier, Trump had a lot to say about Broward County's elections process as a whole.
"The rejects will go individually before the canvassing board and we'll look at each one individually to decide yes that is a reject and this vote can count", Doyle said.More news: Samsung reveals foldable phone, Latest World News
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Elections officials in Broward County, where Democrats have a large advantage, were still reviewing ballots Thursday.
Scott filed lawsuit against Broward County Supervisors of Election Brenda Snipes Thursday night, asking the court to order Snipes to turn over several records detailing the counting and collection of ballots. Under Florida law, a recount is mandatory if the winning candidate's margin is less than 0.5 percentage points. Jeff Weisner, an investigative reporter for ABC affiliate Local 10 News, confronted Snipes on camera about what is taking so long to tabulate vote counts, to which she explained that other "counties didn't have 600,000 votes out there".
As the prospects of recounts in Florida's Senate and governor's races grew yesterday, he told reporters at the White House that "really bad things" were going on in a county whose untallied votes are crucial to both contests.
"It's a mob scene", said William Scherer, a Republican attorney representing Scott and who worked for George W. Bush in the recount during the 2000 presidential election.
As Scott announced his lawsuits, questions began to be asked about ballot papers which did not clearly indicate how to vote in the Senate election.
Snipes was again found guilty of violating election law in February, when a Florida judge found that she prematurely opened a number of mail-in absentee ballots.
Elias said it isn't "appropriate" for Scott to initiate a law enforcement investigation into vote counting when the governor is on the ballot as a candidate for Senate. Scott's election night 56,000-vote margin over Nelson shrank to just over 15,000 votes -- within the margin that triggers an automatic recount -- by Thursday night.