The recanvassing continued anyway, and Al Gore's advisers said they would appeal the ruling.
Circuit Judge Terry Lewis issued his brief order as officials in all 67 Florida counties were preparing to begin the tabulation of about 2,500 overseas absentee ballots.
Bush holds a 300-vote lead in the state that will decide the winner of the presidential election, and Harris is expected to certify a winner - subject to yet another court challenge - once the overseas votes are counted.
Both sides in the election contest assume that Bush will benefit when the overseas votes are counted, making Gore's attempt to win recounts of more than 1 million ballots critical to his effort to overtake his rival.
In Broward County, the area around Ft. Lauderdale, officials said Gore had a gain of 25 votes, with the recount completed of 102 of 609 precincts. A separate recount was underway in Palm Beach County, and Democrats hoped to launch one later in Miami-Dade.
Lewis' court order, read by a court clerk and broadcast live nationally, was succinct.
Based on the ``limited evidence presented, it appears that the secretary has exercised her reasoned judgment ... applied them to the facts ... and made her decision. My order requires nothing more,'' it said.