After 10 hours of tedious hand-counting of Palm Beach County ballots yesterday, Vice President Al Gore closed to within fewer than 300 votes of Texas Gov. George W. Bush in his quest to claim Florida's 25 electoral votes - enough to give him the presidency.

Bush's lawyers had filed suit earlier in the day in federal court to force an immediate halt to the hand-counting of presidential ballots in Palm Beach and three other Florida counties, maintaining that the Republican presidential candidate and his running mate would "suffer irreparable harm" if the count changed the results of Tuesday's election.

But U.S. District Court Judge Donald Middlebrooks put off a hearing on the Bush suit until tomorrow in Miami, permitting yesterday's vote-counting session. Some 4,600 votes were counted by hand - 1 percent of those cast on Tuesday - and the county's ballots were once again run through machines. Gore picked up 787 votes over his total last Tuesday and Bush 105. Of those new votes, Gore gained 33 from the hand counting yesterday, and Bush 14.

That dropped Bush's overall lead in the state to fewer than 300 votes and prompted Palm Beach County Commissioner Carol Roberts - one of the three Democrats on the county canvassing board - to call for a full manual recount of 470,000 ballots, an action strenuously opposed by Charles Burton, a Democratic Circuit Court judge appointed to the bench by Bush's younger brother, Florida Gov. Jeb Bush.

But Roberts' motion carried 2-1, after she argued that Gore's vote pickup, if extropolated to the full county vote would give him a net gain of 1,900 votes and would "clearly would affect the result of the election."

The events of the day precipitously heightened the rancor surrounding a presidential election whose outcome has not been determined.

In accordance with Florida state law, the campaign of Vice President Al Gore had requested a hand count to examine nearly 80,000 ballots that were not counted in four counties: Volusia, Palm Beach, Broward and Miami-Dade. But Bush and his running mate, former Defense Secretary Dick Cheney, went to federal court, seeking to override the state statute permitting the hand count.

The candidates' suit maintained that by opening the election to the "subjective interpretation of voters' intent," the hand counts would violate the constitutional right to equal treatment under the law by "arbitrarily subject[ing] voters in other counties to unequal treatment."

If the recounts swung Florida's 25 electoral votes to Gore, even temporarily, Bush and Cheney maintained, there would be "serious damage to the legitimacy of the presidential election."

Gore campaign officials dismissed the suit as an incursion into Florida's right to govern its electoral process and predicted that it would be dismissed.

Bush aides have grown increasingly concerned that the hand counts could swing to Gore a state in which the Texas governor officially leads by 960 votes with 66 of 67 counties reporting - and unofficially by 327, according to the Associated Press. Former Secretary of State James A. Baker III, representing the Bush campaign, complained yesterday that hand counting would be inherently subjective and open to "the potential for mischief."

Machines, in contrast, "are neither Republicans, nor Democrats, and therefore can be neither consciously nor unconsciously biased," Baker said, as he announced a lawsuit that "we regret we were compelled to take."

For the Gore campaign, Bush's legal action provided relief from the criticism that the vice president was dangerously dragging out the election's proceedings. Though Democratic supporters had filed at least eight lawsuits challenging the results in Florida, none of those suits was brought by Gore's campaign. Now, Gore aides said, it was Bush who went to court first.

That gave Gore officials what they believed to be the right to claim the moral high ground in a battle that has been as much about public relations as raw vote totals.

"Throughout this process, we have proceeded on a single fundamental principal: We want the votes, all the votes, cast to be accurately and fairly counted," said former Secretary of State Warren Christopher, who is representing the Gore campaign in the Florida recount. "The will of the people expressed in accordance with the Constitution should decide who our next president should be."

Added one senior Gore official: "George Bush is always saying he trusts the people, not the government. Well, now he seems to be trusting a federal judge, not the people."

At the heart of the dispute are nearly 80,000 ballots that might hold the presidency in the balance. Gore carries a razor-thin lead in the popular vote of about 200,000 votes nationally, but the winner of Florida will have captured enough electoral votes to be the next president of the United States.

New totals in New Mexico yesterday shifted that state's five electoral votes out of Gore's column and into the undecided category. Gore also appears to have won Oregon and its seven electoral votes.

Neither of those states matters if Florida can be awarded to one candidate or the other. And the 80,000 discarded ballots loom large. Most of those ballots were disqualified because the voter punched holes by two presidential candidates' names. Democratic officials concede that it would be difficult for a manual recount to determine which candidate the voter intended to back. But 26,000 of the ballots were discarded because the electronic counters did not detect a vote -10,000 in Palm Beach, 10,000 in Miami-Dade and 6,000 in Broward. This means that, in some cases, a discernible mark could be detected by a person where it couldn't be detected by a machine. Volusia undercount figures were not available.

As the manual recount began yesterday of a sample of ballots in Palm Beach County, teams of Republican and Democratic counters could be seen holding ballots up to the light to find holes that might have slipped by a machine.

The Bush campaign strongly maintained yesterday that the machine recounts that have taken place in Florida were more than enough. Baker complained that Florida law provided no standards for the different counties to determine which ballots could be reinstated and on what grounds.

"At this point," Baker said, "a changed result would not be the most accurate result, simply the most recent result."

Baker said the legal action would be dropped if Gore would agree to abide by the final machine count, once overseas absentee ballots are tabulated Friday.

But the Gore camp countered with a timely piece of opposition research: In 1997, Bush signed a Texas law decreeing that in the event of a disputed election, a hand count is preferable to a machine tabulation.

"A manual recount shall be conducted in preference to an electronic recount," Texas law reads.

Moreover, in Seminole County, just north of Orlando, election officials took it upon themselves last week to manually examine discarded ballots during the county's electronic recount. Bush wound up gaining 98 votes in the Republican-leaning county.

For Bush, the perils of the manual count are clear. In a hand recount last year in a local Palm Beach County race, 16 of 369 discarded ballots - or about 4 percent - were reinstated. Two years ago, in Miami-Dade County, about 8 percent of the discarded ballots in a state Senate race were reinstated in a hand recount.

If such percentages held in this case, between 3,200 and 6,400 ballots would be reinstated. And because all four counties conducting manual recounts are heavily Democratic, Gore could easily overcome a Bush lead that for the moment is under 1,000 votes.

Under Florida law, each campaign had 72 hours to request hand recounts, and it appeared yesterday that Bush had missed the deadline to seek manual examinations in Republican counties.