But the EU mission has been criticised for making such a declaration ahead of any official results.
"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'," James Bays, Al Jazeera's correspondent in Kabul, 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 only to 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."
Other independent observers warned that turnout in Taliban strongholds in the south may have been as low as 10 and 25-30 per cent for areas such as Kandahar and Helmand respectively.
One foreign official said that the Election Complaints Commission had so far received 100 formal complaints about irregularities, including "allegations of ballot-stuffing in Kandahar".
Attacks by fighters 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.
Rumours 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.
The Afghan monitoring group also warned that there had been voting irregularities.
"In some places we did see the independent electoral commission's staff, at the local level, they were not keeping to a good level of impartiality. Those places need to be looked at carefully," Nadery told Al Jazeera.
"There were, as an example, issues of underage voting ... not a very large number, but that indicates an irregularity."
In Washington, Barack Obama, the US president, hailed the elections as an "important step forward" for Afghanistan.
Millions of Afghans are thought to have voted in Afghanistan's landmark elections to choose a new president and 420 councillors across 34 provinces.
But Taliban threats kept turnout low, especially in the volatile south where Hamid Karzai, the incumbent president, was expected to do well in the presidential race among fellow Pashtuns.
Election observers say a second round between Karzai and Abdullah Abdullah, a former foreign minister who draws much of his support from Tajiks in the north, could divide the country along ethnic lines and lead to unrest.
Richard Holbrooke, the US special representative for Afghanistan and Pakistan, moved to ally fears of possible ethnic conflict, telling reporters with him in Kabul that the two had vowed they would respect the election outcome.
"They're all putting their own views, but they all said they would respect the process," Holbrooke said.
Both Karzai and Abdullah claimed victory in the presidential race on Friday, with the rival camps saying their candidates were on track to win an outright majority of more than 50 per cent and avoid a second round run-off vote in October.
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.