KABUL — Millions of Afghans defied threats yesterday to cast ballots in the country's second national elections since Taliban rule, but turnout appeared weaker this time because of continuing violence, fear and disenchantment. In much of the Taliban's southern strongholds, many people did not dare to vote, bolstering the hopes of President Hamid Karzai's chief rival.

At least 26 people were killed in election-related violence, fewer than had been feared.

Officials began counting millions of ballots as soon as the polls closed at 5 p.m. First preliminary results weren't expected for several days, and some major candidates — including former Foreign Minister Abdullah Abdullah, Karzai's main challenger — already were alleging fraud.

A top election official, Zekria Barakzai, estimated that 40 to 50 percent of the country's 15 million registered voters cast ballots — far lower than the 70 percent who voted in the presidential election in 2004.

Nevertheless, many Afghans did vote, some at great risk to their lives. Authorities managed to open 6,202 polling centers — 95 percent of those planned, according to Barakzai.

The top U.N. official in the country, Kai Eide, said the election "seems to be working well," and NATO Secretary-General Anders Fogh Rasmussen hailed the balloting as "testimony to the determination of the Afghan people to build democracy."

Karzai, a Pashtun tribal leader who has held power since a U.S.-led invasion ousted the Taliban in late 2001, was favored to finish first among 36 official candidates. A strong showing by Abdullah could force a runoff if no one wins more than 50 percent.

The turnout also was modest in southern Helmand province, where thousands of U.S. and British troops — including Kane'ohe Bay Marines — are battling the Taliban.