Peter Erben, chief electoral officer for the joint Afghan-UN election commission, on Tuesday said counting would start slowly but accelerate on Wednesday and Thursday.
Donkeys, camels, horses and helicopters helped bring ballot boxes across deserts and mountains after one of the most logistically tricky polls ever organised by the United Nations.
At Kabul's counting centre, trucks laden with ballot boxes were checked by a bomb-sniffing dog before being unloaded by teams who stacked the boxes in long lines in huge hangar-like warehouses.
International election workers scurried about yelling into walkie-talkies, making sure boxes were put in the right rows.
About 30 people, most candidates' agents, watched as the blue plastic and metal seals on the first boxes were cut and their contents tipped on to a table. Counting is expected to take 16 days and final results will not be declared until 22 October.
An EU election observer mission said the polls had been generally well administered and peaceful and marked "a significant step forward for Afghan democratic development".
Erben said there had been no significant security incidents.
Ballot boxes were brought in for
counting from remote areas
But there was a delay in the eastern province of Nangarhar because of difficulties in bringing ballots from neighbouring Nuristan and Kunar and a rocket attack in the provincial capital, Jalalabad, where counting is to take place.
Police said two rockets hit the city, one striking a government building wounding a guard, and another damaged a house and slightly hurt a child.
In Nangarhar on Sunday, a truck carrying ballots was hit by a roadside bomb. No one was hurt and the boxes were not damaged.
The Taliban had called on voters to boycott the polls, but failed to derail them despite months of violence in which more than 1000 people have been killed. At least 14 people died in violence at the weekend, but voting was overwhelmingly peaceful.
About six million of more than 12 million registered voters cast ballots in what was the final stage of an international plan to bring democracy, launched after US-led forces ousted the Taliban in 2001.
Osama bin Laden's deputy, Ayman al-Zawahri, denounced the polls in a video shown on the Aljazeera television channel on Monday, saying they were not free and took place under US occupation.
Meanwhile, the commander of US forces in Afghanistan warned that more fighting could be expected in the weeks ahead, despite the Taliban's failure to derail Sunday's vote for a national assembly and provincial councils.
"The need for the international community to have commitment here and patience is absolutely essential"
Lt Gen Karl Eikenberry,
Commander of US-led forces in Afghanistan
Lieutenant-General Karl Eikenberry said US-led forces would stay on the offensive this autumn and winter, and while hailing the elections as a success, said Afghanistan and its allies could not afford to rest on their laurels.
He said the focus now needed to be on building security, governance, the justice system and post-war reconstruction, to build a society Afghans would fight to defend.
"The need for the international community to have commitment here and patience is absolutely essential," he said.