KABUL, Afghanistan (AP) — Afghans and the international community hailed its presidential election as a triumph of democracy over violence Sunday, despite complaints about ballot shortages and sporadic fraud after millions of people braved a Taliban threat to vote for a new president. But some cautioned against declaring a premature defeat of the Islamic militants.

Securing the vote was a test for Afghan government forces as they prepare to take full responsibility for their own security as the U.S. and allied forces end their combat mission at the end of this year. The consensus was that they largely passed, though there was sporadic violence.

A roadside bomb hit a pickup truck transporting ballot boxes Sunday in the northern province of Kunduz, killing three people, officials said. But the major attacks that had been feared did not materialize.

“This in itself is a victory over violence and a victory over all those who wanted to deter democracy by threats and violence,” said Thijs Berman, the head of the European Union’s election assessment team in Kabul.

Electoral officials, meanwhile, urged patience, saying officials continued to log complaints and tally ballots. The ballots were coming from more than 20,000 polling stations nationwide, some in extremely remote and rural areas. They were being transported to tally centers in all 34 provinces before the results reach Kabul.

Some candidate forecasts and partial results are expected in the coming days. Noor Mohammad Noor, a spokesman for the Independent Election Commission, said preliminary results were due April 24 and final results will be announced May 14.

With a crowded field of eight candidates, nobody was expected to get the majority needed to win outright. That would force a runoff between the top two vote-getters, which would be held at the end of May. President Hamid Karzai was constitutionally banned from seeking a third term.

Noor said initial reports show a turnout of more than 7 million people, nearly 60 percent of eligible voters. That was sharply up from the estimated 4.5 million people vote in 2009’s presidential and provincial council elections, which were marred by widespread vote-rigging.

The Taliban had warned voters to stay home, saying election workers and polling centers were fair game. A spokesman for the group, Zabihullah Mujahid, claimed in a statement Sunday that more than 1,000 attacks took place “to disrupt the fake and predetermined elections set up by America.” The group often exaggerates its claims.

A number of high-profile attacks before Saturday, including two on offices of the Independent Election Commission and several targeting foreigners, heightened concern. Hundreds of thousands of Afghan security forces fanned out and erected checkpoints at intersections, searching cars and people. Workers also patted down voters, in some cases three times, before they entered polling stations.

Martine van Bijlert, co-director of an independent research group called the Afghanistan Analysts Network, said the days ahead would be key to determining if the Taliban failed to disrupt the vote or if they purposefully laid low on due to the heavy security measures.

“There’s always the possibility that they decided to stage attacks before the elections, before the country went into maximum security mode, and after the elections,” she said.

Brig. Gen. Daniel O’Donohue, the chief operations officer for NATO-led forces, said Afghan voters had done their job and called on candidates and other political players to foster stability.

“The enemy, after this defeat, will surely intensify its senseless violence and the prospect for peace is still precarious — but there is hope and that is everything,” he said in an email.

After an aggressive campaign, three front-runners emerged: Abdullah Abdullah, who was Karzai’s main rival in 2009; Ashraf Ghani Ahmadzai, a well-known academic and former World Bank official; and former Foreign Minister Zalmai Rassoul. They all expressed confidence after the vote that they would win, or at least advance to a second round, but all promised to respect official, “credible” results.

Rassoul, who critics alleged was Karzai’s choice, denied he had any help from the government.

“If the election goes to the second round, we are ready to go to the second round, and if we go to the second round I am confident that we will win,” he told reporters Sunday.

Fears of fraud, such as ballot box stuffing and government interference, were high after the last presidential election. This time, most of the candidates deployed thousands of observers to monitor polling centers.

The official panel overseeing complaints said people have until the end of the day Monday to report any suspect issues. So far, the Electoral Complaints Commission received 2,000 complaints ranging from polling centers running out of ballot papers, interference by election workers and government employees and in some cases by the observers themselves, spokesman Nadir Mohsini said.

Nader Nadery, executive director of the Free and Fair Election Foundation of Afghanistan, said the level of irregularities was much less than had been anticipated and the large crowds and high numbers of observers had acted as a deterrent to fraud.

“The transparency of this election was higher,” he said.

Kim Gamel, Associated Press

Kim Gamel can be followed on Twitter at www.twitter.com/kimgamel.

Associated Press writers Rahim Faiez and Amir Shah contributed to this report.