Democrat Andrew Gillum, who had sought to become Florida's first African-American governor, has conceded after a recount showed he had no way of catching his Republican rival Ron DeSantis, an ally of United States President Donald Trump.

Key points: A machine recount put Mr DeSantis ahead of Mr Gillum by 0.41 per cent

A machine recount put Mr DeSantis ahead of Mr Gillum by 0.41 per cent A separate recount in the race between Democrat Senator Bill Nelson and outgoing Republican Governor Rick Scott is ongoing

A separate recount in the race between Democrat Senator Bill Nelson and outgoing Republican Governor Rick Scott is ongoing The 2000 presidential race between Republican George W Bush and Democrat Al Gore was also subject to a recount

Mr Gillum, the 39-year-old liberal mayor of Tallahassee, had initially conceded the race on the night of the November 6 election to Mr DeSantis, a conservative former congressman.

But he later withdrew that concession when the results showed the two were close enough to trigger an automatic recount.

"This has been the journey of our lives. We've been so honoured by the support that we've received," Mr Gillum said in a video statement.

"Stay tuned, there will be more to come. This fight for Florida continues."

Mr DeSantis, 40, said on Twitter, "This was a hard-fought campaign. Now it's time to bring Florida together."

After a machine recount ended this week, official results showed Mr DeSantis with a lead of 33,683, or 0.41 per cent.

By the weekend that margin appeared impossible for Mr Gillum to overcome.

"We wanted to make sure that every single vote including those that were undervotes, overvotes, as long as it was a legally cast vote we wanted those votes to be counted," Mr Gillum said.

Ron DeSantis is a former congressman. ( AP: Phelan M Ebenhack )

Multiple legal challenges filed in Florida

His stance echoed similar appeals from fellow Florida Democrat, senator Bill Nelson.

Numerous legal challenges were filed in Florida over how to deal with certain ballots and the deadlines for counties to review them.

A recount is continuing in the race between Mr Nelson and his challenger for the Senate seat, outgoing Republican Governor Rick Scott.

After an electronic recount was completed, Mr Scott held a narrow lead.

Officials have until noon on Sunday (local time) to tally any votes missed by electronic voting machines.

That recount has become the subject of an intense political battle, with Republicans, including Mr Trump, claiming without evidence that the process was marred by fraud.

Both parties and their supporters filed multiple lawsuits challenging the process, with Republicans urging a strict standard on which votes were counted while Democrats contested rules that they saw as disenfranchising voters.

The drama of counties across the state recounting ballots brought back memories of Florida's 2000 presidential recount.

In that election, the winner of the White House hung in the balance for weeks before the US Supreme Court stopped the counting and Republican George W Bush triumphed over Democrat Al Gore.

Reuters