Both Karzai and Abdullah claimed victory on Friday, following Afghanistan's landmark elections to choose a new president and 420 councillors across 34 provinces.
The rival camps said their candidates were on track to win enough votes for an outright majority of more than 50 per cent and avoid a potentially destabilising second round run-off vote in October.
The claims were based on unofficial observations by thousands of campaign workers at the 6,200 polling stations.
Afghanistan's independent election commission later demanded that the candidates stop making predications about the result, preliminary figures for which are not now expected before Tuesday.
Final, official returns are due in early September.
Millions of Afghans voted in what was the country's second-ever direct presidential election, but Taliban threats kept turnout low, especially in the volatile south where Karzai was expected to do well among fellow Pashtuns.
Election observers say a second round between Karzai and Abdullah, who draws much of his support from Tajiks in the north, could divide the country along ethnic lines and lead to unrest.
"Everybody understands there is an ethnic issue in the country," Holbrooke said.
"It's a factor, it's not a concern. Is it a factor that gives us heartburn? No, but it is a factor."
The chief European Union election observer, the largest foreign observer force in the country, called the elections fair overall, but said the vote had not been free in some parts of the country due to Taliban intimidation.
"Free was not the case in some parts of the territory due to terror installed," Philippe Morillon said.
"Fair - generally what we have observed was considered by our observers with our methodology good and fair"
chief EU election observer
"Fair - generally what we have observed was considered by our observers with our methodology good and fair."
But the EU mission has been criticised for making such a declaration on the elections ahead of any official results, James Bays, Al Jazeera's correspondent in Kabul, said.
"In their findings there were quite a lot of problems, yet at the top of their report [was] their conclusion: 'the holding of elections in Afghanistan a victory for the Afghan people'," Bays said.
"But I've spoken to other observers, not from the EU, and they say they are very, very surprised that the EU is hailing this as a success.
"They say its not right to hail it as a success until we have the final results, until we see whether there are any complaints and until we view the complaints procedure."
The EU monitoring mission admitted that it had struggled to visit polling stations, managing to only get to six polling locations across the south of Afghanistan.
Wadir Safi, a professor of law at Kabul University, said that international monitoring efforts had been insubstantial.
"The monitoring system was not visible at all, especially the international monitoring system. [At] Kabul University, which I saw myself, it was very late and it was not even necessary to monitor the students - they know how to vote," he told Al Jazeera.
"In the other constituencies, especially the provinces - no monitoring groups have gone there."
'Violence and intimidation'
Insurgent attacks during polling claimed more than two dozen lives in what EU observers said were 270 security incidences.
Nader Nadery of the Free and Fair Election Foundation of Afghanistan, an Afghan vote monitoring group said the Taliban in the country's south had cut off the fingers of two voters.
Rumors that the Taliban would cut off the fingers of voters - identified by purple indelible ink, used as an anti-fraud measure to show who has already voted - spread ahead of the elections.
But after the dramatic escalation in violence in the weeks leading up to the election, Afghan and US officials breathed a sigh of relief that polling was relatively peaceful.
In Washington, Obama praised the vote as a move in the right direction. But he warned that Taliban violence may continue as official results are finalised.
"Over the last few days, particularly yesterday, we've seen acts of violence and intimidation by the Taliban, and there ... may be more in the days to come," he said.
Polls conducted before the election showed Karzai in the lead, but not by enough to avoid a run-off.