TALLAHASSEE, Fla. — Andrew Gillum, the Democratic nominee and mayor of Tallahassee, conceded the Florida governor’s race on Saturday to Ron DeSantis, a former Republican congressman closely allied to President Trump, saying he was satisfied with a recount that had him trailing by about 34,000 votes.

Mr. DeSantis declared victory on election night this month, and Mr. Gillum, 39, announced he was conceding the race at the time. But he re-entered the race a week ago, under pressure from staff members and allies in organized labor, after the Florida secretary of state’s office declared an automatic recount.

“We promised to fight until every vote was counted, and obviously we are now closing out the hand recount phase,” Mr. Gillum said in an announcement broadcast over Facebook Live on Saturday, standing next to his wife. “R. Jai and I wanted to take a moment to congratulate Mr. DeSantis on becoming the next governor of the great state of Florida. This has been the journey of our lives.”

Mr. Gillum has not yet called the governor-elect, a spokesman for Mr. DeSantis said. But Mr. DeSantis responded to Mr. Gillum on Twitter, accepting his concession anew.