The Gore campaign has demanded a "hand-count" of the voting in four Florida counties where it claims thousands of Gore voters were disenfranchised by confusion over the ballot paper used.
This demand came as a machine recount of the seven million votes cast in the whole of Florida on election day was still going on in the state capital of Tallahassee.
The original count showed Governor George Bush ahead by 1,784 but this figure was being reduced as the recount continued yesterday.
Mr William Daley, the chairman of the Gore campaign, has accused the Bush campaign of "trying to presumptively crown themselves the victors". He said that "trying to put in place a transition runs the risk of dividing the American people and creating a sense of confusion."
Mr Bush has indicated he and his running mate, Mr Dick Cheney, are ready to go ahead with organising the transition from the Clinton Administration as soon as the recount ends and if he was confirmed as president. Mr Daley appealed to the Bush campaign to "let the legal system run its course and let the true and accurate will of the people prevail."
He denied charges the Gore campaign is trying to "drag out" the process of electing the president. "All we are seeking is that the candidate that the voters preferred becomes our president. That is what our Constitution demands."
He said "We will move this matter ahead as quickly as possible. We do not want delay but we want democracy fulfilled."
Mr James Baker, the former secretary of state, who heads the Bush campaign team of observers, strongly denied that the Palm Beach voters who complained about the ballot card were disenfranchised.
"They did have a chance to have their voices heard. And let me tell you something else about that ballot: it was posted as required by Florida law in newspapers and public places all over the state of Florida.
"Not one complaint was received about that ballot, which by the way was approved by a Democrat who was elected . . . we haven't heard one gripe about that ballot until after the voting took place," Mr Baker said in Tallahassee. The eyes of the US and the rest of the world are on Florida as recounts and court actions decide who will be the next president. But although the first recount was to end last night, the waiting period will continue.
The Florida Secretary of State is being advised not to certify the result of presidential election voting in the state until the prescribed waiting period of 10 days to allow overseas ballot to arrive has elapsed. That would delay a final result until November 17th.
To complicate the matter further, a number of court actions challenging the results in various parts of the state are likely to go ahead and this could cause further delays.
The recount results were being centralised in Tallahassee with small armies of lawyers and political advisers from the Bush and Gore campaigns as observers. The Gore team is headed by the former secretary of state, Mr Warren Christopher.
Vice-President Al Gore has returned from his home state of Tennessee to Washington where his aides are setting up a special office to organise possible appeals against the election result. Mr Daley said the response of the Bush campaign to the charges of voter confusion was "blithely to dismiss the disenfranchisement of thousands of Floridians as the usual sort of mistake made in an election."
Much of the post-election confusion and anger of voters in Florida are centred on Palm Beach County, where there are numerous complaints about the format of the ballot paper.
Three voters have filed a complaint in a federal court asking for an injunction to freeze the situation and a new election in the county.
Some 19,000 ballot papers have been declared invalid because voters punched the holes for two names among the Presidential candidates.
Voters complain that they were confused by having the punch holes for Mr Gore and the Reform Party candidate, Mr Pat Buchanan, too close, and they may have tried to correct their vote by punching the ballot card twice.
Mr Buchanan received 3,407 votes in Palm Beach, which is an affluent area with a large number of retired persons who tend to be Democratic supporters. This is 10 times the number of Reform Party voters registered in the county. It is also 20 per cent of the vote Mr Buchanan received spread over the state's 67 counties.
Mr Buchanan has expressed unease at the situation, telling NBC's Today show: "My guess is I probably got some votes down there that really did not belong to me and I do not feel well about that. I don't want to take any votes that do not belong to me."
Mr Daley said thousands of voters "thought they were voting for Al Gore and had their votes counted for Pat Buchanan."
The Rev Jesse Jackson told a meeting of disgruntled voters the issue "was not about black and white but about wrong and right."
Other protesters paraded in Palm Beach with placards denouncing the ballot papers.
Another reported anomaly is that 100,000 voters did not vote for President although they filled in their choices for other elections on the same ballot paper. Again this could be due to voters not using the punch-ballot mechanism correctly and this could only be detected by a lengthy hand count.
The National Association for the Advancement of Coloured People has urged the Department of Justice to investigate the Florida election, saying it has received more than 300 complaints.
Some of these said it was difficult to vote for Mr Gore because of the design of the ballot paper.
The Attorney General, Ms Janet Reno, said in Washington she is ready to review any eventual complaint about the count but said so far she had no reason "to jump in". "We are not here to generate controversy. We are here to do what's right, to make sure the voice of the American people is heard, and that basically is a matter of state law."
In Pinellas County on Florida's west coast, election workers also launched a second recount when the first recount produced a swing of more than 400 votes to Mr Gore, officials said.
Under Florida law, state judges have wide-ranging powers in the cases of electoral challenges. In some cases judges have been known to adjust results of contested elections based on new facts that are brought forward.
In 1998, the mayoral election for Miami was challenged. The judge then rejected the man who was elected and awarded the mayoralty to the present mayor, Mr Joe Carollo.