U.S. District Judge Donald Middlebrooks said the question of halting recounts is not a matter for federal courts and properly belongs in state court.
``While I share a desire for finality, I do not believe it is served'' by involving a federal court, he said after hearing arguments from lawyers representing George W. Bush and Vice President Al Gore.
The ruling, which Middlebrooks himself said was likely to be appealed by the Republicans, marked the latest turn in a presidential election now one week past the balloting with no end in sight.
The winner of Florida's 25 electoral votes stands to gain an Electoral College majority and become the nation's 43rd president.
Bush has a 388-vote lead in an unofficial tally by the AP, but Middlebrooks' ruling clears the way, temporarily at least, for either side to seek additional hand recounts that could affect the count.
The ruling came a short while after Florida's top election official pledged to wrap up the vote recount by late Tuesday afternoon. Democrats suggested she was motivated by her Republican affiliation, and her effort to meet the deadline was thrown into doubt by the legal maneuvering in at least two courtrooms around the state.
Speaking from the bench, Middlebrooks said the procedures for manual recounts appear to be politically neutral. Republicans had argued that a manual recount in just a handful of counties selected by the Democrats - rather than all 67 - would dilute the vote of people elsewhere around the state.
He said he considered that a serious argument but insufficient to warrant intervention.
Earlier, Middlebrooks had signaled clearly he understood the gravity of the case before him and the likelihood his decision would be appealed.
``I am not under an illusion I am the last word on this, and I am rather grateful for that,'' he said.
The judge made his observation as state election officials promised to press ahead with plans to finish counting by Tuesday at 5 p.m. and certify a winner by Saturday, after an unknown number of overseas absentee ballots are rolled into the totals.
``The law unambiguously states when the process of counting and recounting the votes cast on Election Day must end,'' Katherine Harris, Florida's secretary of state, said in a written statement distributed in Tallahassee.
``For this election, that time is 5 p.m. Nov. 14, which is tomorrow.''
Both sides seemed to be guessing that the Texas governor's margin would grow when the overseas votes were tallied by Friday afternoon.
That made the hand recounts, and the court arguments, critical. Already, officials in Volusia and Palm Beach counties were deep into hand recounts. Officials made provisions to sort through thousands of ballots in Broward County on Monday, and in Miami-Dade, the canvassing board set a meeting for Tuesday to decide how to proceed.
The attorneys couched their arguments to Middlebrooks in much the same terms the two sides have used in public statements since the Florida dispute flared in the hours after the polls closed last week.
``The process, to sum it up, is selective, standardless, subjective, unreliable and inherently biased,'' said GOP lawyer Theodore Olson.
Olson said the hand count introduced elements of chance and partisan bias to what ought to be a simple and uniform process of checking Florida's extraordinarily close election result.
Bruce Rogow, lawyer for the Democratic side, said the hand count increased democracy and accuracy.
``Is it messy? Does it go on and on in some fashion? Yes, yes it does, but that is democracy.''
Rogow and other Democratic lawyers disputed GOP claims that the hand counts could go on for weeks, saying they will almost certainly be complete by Friday.
The day began with Harris, a Republican, meeting with officials from the two campaigns.
Her decision to require counties to certify results on Tuesday prompted a sharp retort from Warren Christopher, representing the Gore campaign. He suggested that she was biased because of her political affiliation and her association with the state's GOP governor, Jeb Bush, the presidential candidate's brother.
``We regard the action of the secretary to be arbitrary and unreasonable,'' he said.
He said the county election boards and the Gore campaign would appeal promptly, and officials in Volusia County filed papers in state court seeking to extend the Tuesday deadline.
Officials in some counties said they could not physically complete the Gore-sought hand recounts by the deadline.
The gist of the Republican claim is that the hand recounts in only four of Florida's 67 counties amount to unequal treatment for some Florida residents. The 14th Amendment guarantees all Americans equal protection under the law.
Under Florida law, manual recounts are allowed if a candidate meets a post-election deadline to request them and the local election board agrees.
The Bush camp argues that hand recounts are a sort of third election - after the regular Nov. 7 voting and an automated recount that took place last week.
If Bush fails in court, senior strategists say he may seek his own recounts in some GOP-dominated Florida counties. Bush also could demand recounts in close-voting states won by Gore, such as Iowa, Wisconsin, Oregon - or too-close-to-call New Mexico.
Former Secretary of State James A. Baker III, who is leading the Florida legal and public relations effort for Bush, described the Florida standoff as ``a black mark on our democracy and on our process.''
Christopher, former secretary of state in the Clinton administration, portrayed vote recounts as a small necessity of democracy.
``If at the end of the day, George Bush has more votes in Florida than we do, certainly the vice president will concede,'' Christopher said.
Gore leads in the nationwide popular vote, but the Electoral College tally is so close that the eventual winner in Florida is almost certain to win the White House.
Bush would have to win Oregon, Iowa, New Mexico and Wisconsin to claim the White House without Florida - a long shot given that Gore is leading by 5,000 or more votes in all those states but New Mexico.
Apart from Florida, Bush carried 29 states for 246 electoral votes. Gore, who added Oregon to his column on Friday, counted 19 states plus the District of Columbia for 262 electoral votes, with 270 needed for victory.