KABUL, Afghanistan — Plastic crates loaded with ballots arrived at counting centers Sunday as Afghan officials began tallying results from a historic presidential election that largely defied fears of low voter turnout and Taliban violence.

Preliminary results are still days away, officials said, as ballot boxes traveled by donkey cart, truck and helicopter to reach counting stations in Afghanistan’s 34 provinces. Some 7 million voters, far more than in the two previous nationwide elections, cast ballots Saturday to determine the successor to President Hamid Karzai, who is constitutionally barred from extending his 13-year tenure.

A roadside bombing in the northern province of Kunduz struck a vehicle being used by election officials, killing a police officer and two poll workers and destroying an unspecified number of ballot boxes, officials said. The ballot boxes were being brought from a rural area to the provincial capital to finalize counting.

Election officials pleaded for patience and urged the eight candidates to respect the final results, which were expected to be certified in mid-May. If no candidate receives an absolute majority, as is expected, a runoff between the top two vote-getters would take place no earlier than May 28.

The vote-counting is being closely watched in Washington and across the world after the previous presidential election, in 2009, was marred by widespread voter fraud and ballot stuffing. Election officials instituted new measures this year to track ballots and report possible irregularities, and candidates deployed thousands of observers to polling places.

“Vote counting has been conducted very well all over Afghanistan, except in distant and insecure provinces,” Zia-ul-Haq Amarkhail, an official with the Independent Election Commission, told reporters. “Despite the insecurity, the materials are secure and safe under the watch of IEC employees and security forces.”

Although the leading candidates said they had received reports of irregularities, they pledged to wait for the results of official investigations.

Zalmai Rassoul, a former foreign minister who is seen as one of the front-runners, told reporters he would respect the results and denied reports that he had received illicit help from members of Karzai’s government. A longtime adviser to Karzai, the septuagenarian Rassoul is believed by many Afghans to be the current president’s choice to succeed him.

“If the election goes to the second round, we are ready to go to the second round,” he said. “And if we go to the second round, I am confident that we will win.”

While turnoutmore than half of the estimated 13 million eligible voters went to the polls nationwide — was robust in Kabul and other urban centers, a mixed picture was emerging from rural areas and Taliban-controlled districts where many polling stations did not open due to insecurity or voters staying home out of fear.

In Logar province, south of Kabul, officials in the district of Baraki Barak said that six out of 19 polling stations that were supposed to be in service Saturday did not open at all. Many of those that did faced sporadic rocket fire from Taliban insurgents holed up in surrounding areas, said Haji Mohammad Fareed Samanderi, head of the local council in Baraki Barak.

Just west of Kabul, in the insurgent-plagued province of Wardak, barely half of 38 polling stations in Sayedabad district opened, and most of them saw low turnout of about 50 to 70 voters each, said a member of the local council there, Mohammad Qais. The Interior Ministry said Saturday that it arrested police and intelligence officers for stuffing five ballot boxes at one polling place in that district.

Mohammad Shafiq, a member of the elected council for the eastern province of Khowst, said no polling stations opened in remote areas because of Taliban threats to harm anyone who participated. The day before the vote, two Western journalists working for the Associated Press were shot by a police officer in rural Khowst; one, German photographer Anja Niedringhaus, was killed.

“Since most of the areas in those districts are controlled by the Taliban, the people were afraid that they might be killed in the future” if they came out to vote, Shafiq said by phone.

Experts said the disparity in turnout made it even more crucial that the counting process is seen to be fair, so that voters in remote or Taliban-dominated areas don’t feel as if they were shut out of an election that could determine Afghanistan’s political direction and relations with the West for years.

“It’s a little bit of a rural-urban divide, but it’s more about who controls the area and how free people feel,” said Martine van Bijlert, co-director of the Afghanistan Analysts Network, a Kabul-based independent research organization.

“If the people couldn’t vote but they see the outcome as representing more or less how they wanted to vote, it becomes less of an issue.”

shashank.bengali@latimes.com

Twitter: @sbengali

Baktash is a special correspondent.