Afghanistan will hold a deciding round of its problem-hit presidential poll on 7 November, pitting Hamid Karzai against his rival Abdullah Abdullah.
News of the run-off vote follows weeks of mounting international pressure.
It comes a day after a UN-backed panel said it had clear evidence of fraud in August's first round, lowering Mr Karzai's vote share below 50%.
Mr Karzai told a news conference that he accepted the findings, adding they were a "step forward" for democracy.
Mr Abdullah, speaking to the BBC, also said the move would "help democracy in this country and strengthen the faith of the people in the democratic process".
Initial results suggested Mr Karzai, the incumbent, had received 55% of the vote, and ex-Foreign Minister Mr Abdullah 28%.
But the UN-backed Electoral Complaints Commission (ECC) ordered that ballots from 210 polling stations be discounted.
This meant Mr Karzai's total was reduced to below the 50% plus one vote threshold for outright victory, indicating a second round was needed.
Since the disputed first round of polling, there has been intensive Western lobbying of Afghanistan's leaders to resolve the weeks of political paralysis.
The White House - debating a request for 40,000 more US troops to be sent to Afghanistan - warned at the weekend no more soldiers would be deployed until a political resolution was reached.
Correspondents say it was therefore not surprising to see Mr Karzai give his reaction to the run-off, at a news conference alongside UN envoy Kai Eide and US Senator John Kerry.
"This is not the right time to discuss investigations, this is the time to move forward to stability and national unity," Mr Karzai said.
"I call upon our nation to change this into an opportunity to strengthen our resolve and determination, to move our country forward and to participate in the new round of elections."
Mr Abdullah told the BBC he had telephoned Mr Karzai to thank him for his remarks.
"He talked about national unity and also he stressed on the need for going to the second round which is exactly what I want to do - so that was a courtesy call, a word of thanks," he said.
He added: "I know that there are challenges with it; the security situation, and the winter is coming... but I think the fact that the process is moving now forward rather than being stuck, that in itself I consider it a step forward and we have to face the challenges."
The BBC's Martin Patience, in Kabul, says there will be no guarantee that any new vote will be free of the fraud that dogged the first round.
But for now the political deadlock appears to have been broken, for a couple of weeks at least, our correspondent says.
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