"I am replacing my words of concession with an uncompromised and unapologetic call that we count every single vote," Gillum said at a press conference in Tallahassee on Saturday.
Unofficial election results showed Republican former U.S. Rep. Ron DeSantis ahead of Gillum by less than 0.5 percentage points. Under state law, such a margin requires a machine recount of ballots.
Gillum had conceded the race to DeSantis on Tuesday night.
DeSantis responded by saying the Florida election results are clear and he is moving forward as he prepares to be the state's next governor.
"Those results are clear and unambiguous, just as they were on Election Night," DeSantis, a former congressman, said in a video posted Saturday on YouTube by the Republican Party of Florida.
While DeSantis said it's important to follow state law, he added, "With the election behind us, it's now time to come together as a state as we prepare to serve all Floridians."