But they said a demand by interim president Hamid Karzai's opponents for fresh polls was unjustified.
"Such action would also put into question the express will of millions of Afghan citizens who came out to vote," said the Organisation for Security and Cooperation of Europe (OSCE) on Sunday.
The OSCE had very recently warned that the security situation in Afghanistan made it impossible to monitor the elections in a "meaningful" manner.
The Free and Fair Election Foundation of Afghanistan (FEFA) - an independent Afghan poll monitoring board that had in excess of 2300 observers covering Saturday's election - also urged poll organisers to ensure the counting process went more smoothly.
FEFA chairman Dr Muhammad Said Niazi told a news conference in the Afghan capital that it had yet to be determined whether confusion over the pens used at voting centres was a technical problem or a violation of electoral rules.
"We are suggesting an open investigation," Niazi said. "If the issue of the ink was really not a mistake then the legitimacy of the elections can be called into question."
But Niazi said initial reports suggested the election was largely free and fair.
Security during voting was
heightened across the country
"The turnout of people in different parts of the country, especially the active participation of women, is the reason for what we are stating," he said.
On Sunday, ballots were being brought to eight counting centres around the country and election workers began the tally. Officials say very early results could emerge late on Sunday or early on Monday.
Polling stations were issued with two types of pens - one for the voter to mark a ballot paper and the other for the voter's finger to be indelibly stained to show they had cast their ballot.
There were widespread reports of the wrong pens being used until the UN-Afghan Joint Electoral Management Body (JEMB) said it intervened and fixed the problem a few hours after voting started.
Although the observers' statements may come as a welcome relief to Karzai, it remains to be seen whether his rivals will accept them.
All of Karzai's rival candidates announced midway through Saturday's voting they were boycotting the election and would not recognise the result because of the row, in effect leaving only Karzai in the race.
The wrong pens were used to
mark voters' fingers
Opposition candidates met in Kabul and signed a petition saying they would not recognise the vote results.
"This vote is a fraud and any government formed from it is illegitimate," Uzbek candidate Abd al-Satar Sirat said.
Islamic poet Abd al-Latif Padran, another candidate, said: "Today was a very black day. Today was the occupation of Afghanistan by America through elections."
Ethnic Hazara candidate Muhammad Muhaqiq told a news conference that an electoral commission should be formed to examine the vote. However, he indicated he might accept a compromise.
"We want the United Nations to set up an independent commission, including representatives of the candidates, to investigate this ink and to come to a decision," Muhaqiq said.
"If the result of the investigation is satisfactory, then the commission should rule that the elections were legitimate. If not, then the vote was not legitimate."
Even if the vote is validated, Karzai's ability to unite the nation, fight rampant "warlordism" and crush the Taliban insurgency might be fatally compromised if his opponents refuse to recognise the vote's legitimacy.
"The election was free and fair. It is very legitimate"
Afghan interim president
Karzai, the US's favoured candidate who is widely tipped to win the contest, said yesterday: "The election was free and fair. It is very legitimate.
"Who is more important, these 15 candidates, or the millions of people who turned out today to vote?" Karzai asked.
His comments were echoed by Zalmay Khalilzad, Washington's man in Kabul. "The Afghan nation has spoken - it has voted for democracy and freedom," he said.
Keen to offer a contrasting image to its continuing troubles in Iraq, with US presidential elections closing in, the Bush administration had wanted to showcase Afghanistan as a success.
If it lasts, the opposition boycott will constitute a huge blow and vindicate critics who accused the US of rigging the whole process to engineer a Karzai triumph.