The Gore campaign had asked the court to order an immediate recount - Leon County Circuit Court Judge Sanders Sauls rejected that request, but ordered that the disputed ballots be brought to the court pending Saturday's hearing.
Mr Gore called on Tuesday for a recount of thousands of what he believes to be questionable ballots in the state of Florida.
The outcome of the state-wide vote in Florida will almost certainly determine which candidate is to be sworn in as the next president of the United States on 20 January.
Lawyers representing the two sides are continuing to file cases concerning the eligibility of vote recounts in various Florida counties, which could erode the narrow lead currently enjoyed by Mr Bush in the state.
"This is not a time for delay, obstruction and procedural roadblocks," the vice-president said.
Mr Bush's spokeswoman, Karen Hughes, countered that Mr Gore simply "wants to go back and change the rules after the counting is over".
Recounts in the balance
Meanwhile a circuit court judge scheduled a hearing on Saturday to decide whether vote recounts are to go ahead in the counties of Miami-Dade and Palm Beach, as requested by Mr Gore's lawyers.
The Gore campaign had asked the court to order an immediate recount - Leon County Circuit Court Judge Sanders Sauls rejected that request, but ordered that the disputed ballots be brought to the court pending Saturday's hearing.
The ballots in question - about 10,000 from Miami-Dade and 3,300 from Palm Beach - had been rejected by mechanical counting devices, and the Gore campaign wants them recounted by hand.
Gore campaign lawyer David Boies said he might appeal against Judge Sauls's ruling, in order to secure an immediate recount of the votes.
With the vote tally throughout Florida already so close, Mr Gore's team hope that a recount in these counties would produce enough Gore votes to swing the state-wide result in his direction.
Bush appeal
In a separate legal move, Mr Bush's lawyers sought to seal their candidate's victory by asking the US Supreme Court to end any further recounts.
The Bush legal team asked the court to overturn a Florida Supreme Court ruling that allowed hand recounting of votes to continue past a state imposed deadline.
Mr Gore's lawyers responded that the Supreme Court should not get involved in the dispute over the presidential recount in Florida.
Cabinet in waiting
Also on Tuesday, Mr Gore criticised Mr Bush for pushing ahead with plans to form an administration to take over the White House.
Mr Gore said naming cabinet appointments was inappropriate until every vote in Florida was included in the final count.
Mr Bush has already set up a transitional team, headed by vice-presidential running mate Dick Cheney.
Mr Cheney is seeking private capital to finance the work, after what he called the "regrettable" refusal of the civil service administration to release funds.
The civil service has also refused to give the keys of the transition offices to the Republican team, on the grounds that - three weeks after the vote - there is still no clear presidential winner.
Mr Gore dismissed opinion polls that show the American public is growing increasingly impatient for a final result in the election, 20 days after voting.
"I am quite sure the polls don't matter in this because it is a legal question," he said.
According to the latest ABC/Washington Post poll, most Americans - including one in four Democratic Party supporters - believe Mr Gore should admit defeat now that Mr Bush has been certified the winner in Florida.
