In an attempt to grab the high ground in the presidential ballot count, Al Gore issued a surprise offer last night to drop any legal challenge to the Florida election if hand recounts are permitted to go forward in three heavily Democratic counties.

But in a dizzying series of events, Florida's Republican secretary of state refused a few hours later to include the hand counts in her official tally.

And George W. Bush, one hour after that, summarily rejected Gore's proposal.

The election should be resolved not by "deals or efforts to mold public opinion," the Texas governor said, but "by the votes and by the law."

Gore, in the first public comment by either candidate after two days of deepening confusion and chaos in Florida, also offered to abide by the outcome of a statewide manual recount, if Bush preferred that alternative.

"The campaign is over, but a test of our democracy is now under way," the vice president said in a hastily announced statement just after 6:30 p.m. His running mate, Sen. Joseph I. Lieberman, was at his side.

Gore extended an invitation for a face-to-face meeting with his Republican rival before the results in Florida are final. That meeting would be intended "not to negotiate" but as a show of national unity, he said.

Bush rushed back to Austin from his central Texas ranch to deliver a response at 10:15 p.m. Like Gore, he read his statement over national TV from his official residence.

Both men projected a statesmanlike tone, saying the nation's interests should come before their own.

But Bush turned thumbs-down on Gore's proposal of a statewide manual count. He said it would make the vote tally "less accurate" because repeated handling of the ballots would introduce further error into the process.

Bush said the Gore proposal was nothing new, even though the vice president offered for the first time to abandon any legal action in connection with the election.

Bush also rejected the Democrat's offer to meet before the tally is complete. He did say he'd be glad to get together with Gore after the election is decided.

In line with efforts by his campaign to bring the dispute to an end by this weekend, Bush made it clear that he expected a winner in Florida to be known by Saturday, when Florida Secretary of State Katherine Harris intends to certify the results.

The vice president's unexpected offer was the first direct effort by either of the candidates to propose an end to the post-election season.

Gore addressed several of the concerns of politicians in both parties, including the fear that a bitter struggle over the election results could poison the atmosphere for whoever wins the presidency.

He urged his supporters and Bush's to "lift up this discourse, to refrain from using inflammatory language and to avoid statements that could make it harder for our country to come together once the counting is over." If he wins, Gore said, he'd be ready to travel to Texas to meet with Bush; if he loses, he added, he'd meet the governor wherever Bush wanted.

Gore also appealed to what polls show is the public's desire to see the matter settled through counting, rather than legal action. He said he would not take or support legal action to challenge the Florida count, if the manual recounts are allowed to continue.

And he spoke to those who want to see the matter resolved quickly by predicting that a "fair and final" outcome could be reached relatively soon under his proposal. Even a statewide hand recount, Gore said, should take no more than a week to complete.

"It's a smart tactic," said John J. Pitney of Claremont McKenna College in Pomona, Calif. "He is trying to seize the rhetorical high ground. On the other hand, he very much wants a process that will be very favorable to his election."