Abdullah Abdullah demanded that the preliminary result, due out on Monday, be delayed for a comprehensive audit of suspicious votes, repeating that he would reject the outcome if his demands were not met.
But Ashraf Ghani, who is reported to be at least one million votes ahead in the count, insisted that the result could not be delayed again and must be revealed by the Independent Election Committee.
The preliminary result will include all votes from the June 14 run-off vote, with the official result scheduled for July 24 after a period for adjudication of complaints.
The dispute over fraud has tipped Afghanistan's first democratic transfer of power into turmoil as US-led troops end their 13-year war against the Taliban, and the country faces a new era with declining civilian aid.
"What we are asking for is thorough auditing, then preliminary results afterwards," Abdullah told supporters in Kabul.
"We are honoured to claim that we are the majority of votes in Afghanistan that are clean. I will accept the result when the clean votes are separated are from unclean votes."
Abdullah's stance came despite reports that the two candidates were close to a deal agreeing that the audit would be held, but only after the preliminary results.
Discussions between the two campaigns were set to continue into the night.
Influential US Senator Carl Levin, on a visit to Kabul, told reporters that he expected a compromise to be reached.
"Tomorrow there's going to be an announcement of the result," Levin, chairman of the Senate committee on armed services, said.
"Something else is going to be announced ... I expect that something else is going to be an agreement on a comprehensive audit.
"We have assurances they will accept the outcome of such an audit."
Ghani's team earlier said that no further delays in the result were unacceptable.
"This is a red line for us," Azita Rafhat, a Ghani spokeswoman, told AFP.
"We gave them enough time, and now the people want to know the result of their votes."
The US and Afghanistan's other international backers had pushed hard for a smooth election as Nato troops pull out, but the fraud allegations have provoked a major political crisis in Kabul.
Any prolonged power struggle would undermine claims that the costly US-led military and civilian mission has helped to establish a functioning state in Afghanistan.
It could also threaten billions of dollars of aid pledges, and boost the insurgents.
The government on Sunday rejected a proposal to ban Facebook during the election deadlock, despite fears that social media postings have fanned ethnic hatred.
Ghani attracts much of his support from the Pashtun tribes of the south and east, while Abdullah's loyalists are Tajiks and other northern Afghan groups, echoing the ethnic divisions of the bloody 1992-1996 civil war.
The United Nations mission in Afghanistan has highlighted the risk of political tensions spilling over into civil unrest, though protests have so far been peaceful.
President Hamid Karzai, who has ruled since the fall of the Taliban in 2001, is constitutionally barred from a third term in office, and he has not publicly endorsed one candidate.
COMMENTS (3)
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ
If Ghani has Pashtoon support, he would win in the millionth recount by million votes a head all the times..
A pacified runner up is important for democracy and peace in Afghanistan. This is happenning the second time with Dr. Abdullah who got 45% votes in round 1. In my opinion, a little delay in announcing results should not be a problem and the grievances of Dr. Abdullah should be looked into. He alleged that some ballot boxes had more votes than the voters in the area. If its true then revoting in those areas should be announced.
On the second hand, Ashraf Ghani's lead should not be doubted as such things happen in democracy. Its possible that those who voted for others in round-1 backed Ghani in round-2. Whether or not Dr. Abdullah becomes president, he will remain very important to Afghan politics and peace process.
It matters not whether Abdullah Abdullah accept or does not accept the vote count. As an Eye specialist, he should better make sure that the Afghans eyesight is improved to be certain who they are voting for? Now be a sportsman and not a spoiler the second time.
Rex Minor