GHAZNI, Afghanistan — The Taliban agreed yesterday to free 19 South Korean church volunteers held hostage since July after the government in Seoul pledged to end all missionary work and keep a promise to withdraw its troops from Afghanistan by the end of the year.

In eastern Afghanistan, a suicide bomber attacked NATO troops helping build a bridge, killing three American soldiers, an American official said.

In striking the deal, the Taliban apparently backed down on earlier demands for a prisoner exchange, but may still emerge politically stronger having negotiated successfully with a foreign government, an analyst said.

Relatives of the hostages in South Korea welcomed news of the deal, which did not specify when the captives would be released.

“I would like to dance,” said Cho Myung-ho, mother of a 28-year-old hostage, Lee Joo-yeon.

The deal was made in direct talks between Taliban negotiators and South Korean diplomats in central Afghanistan. The Afghan government was not party to the negotiations, which were mediated by the International Committee of the Red Cross. A South Korean presidential spokesman, Cheon Ho-sun, said from Seoul that the deal had been reached “on the condition that South Korea withdraws troops by the end of year and South Korea suspends missionary work in Afghanistan.”

South Korea did not appear to commit to anything it did not already planned to do. Seoul has already said it would withdraw its 200 troops in the country by the end of the year and has also sought to prevent missionaries from causing trouble in countries where they were not wanted.

The South Korean government and relatives of the hostages have said the 19 kidnapped South Koreans were not missionaries, but were doing aid work such as helping in hospitals.

Taliban commander Mullah Basheer told a press conference following the talks that the Taliban would say today when and how the captives would be released. They are believed to be held in several different locations.

Missionaries from South Korea and scores of other countries have historically been active in Afghanistan, but there is no way of knowing how many are there now.

Most operate without the knowledge of their governments, and there is some disagreement on the boundaries between missionary work, proselytizing, and Christian-inspired aid work.

An analyst said the Taliban, which has been leading an increasingly bloody insurgency against Afghan and Western security forces, emerged from the hostage crisis with increased political power.

“Maybe they did not achieve all that they demanded but they achieved a lot in terms of political credibility,” said Mustafa Alani, director of security and terrorism studies at the Dubai-based Gulf Research Center. “The fact that the Koreans negotiated with them directly and more or less in their territory … is in itself an achievement.”

Taliban spokesmen have previously said they had no interest in a ransom payment.