The 19 remaining South Koreans being held hostage by the Taliban in Afghanistan will be released over the coming days, following a deal between Seoul and the militants that paves the way for the end of the six-week-long crisis.

The breakthrough came after direct talks in which the Korean government agreed to withdraw 200 members of medical and engineering units helping rebuild Afghanistan by the end of the year and to stop all Korean missionaries from travelling to the Muslim country.

"The Taliban agreed to free the 19 South Korean hostages on the condition that South Korea withdraws its troops within this year and halt missionary activities," said Cheon Ho-seon, the Korean president's spokesman, on Tuesday.

However, the details of the release were still being worked out on Tuesday night and it could take several days before the hostages are freed because they are being held in small groups in various locations.

"The government will do everything possible to make sure the hostages are safely back to their families' arms as soon as possible without delay," Mr Cheon said, adding that Korean officials in Afghanistan had talked on the phone with 12 of the hostages and had been assured that they were safe.

The deal also included Seoul's agreement to withdraw all Korean activists and volunteers from Afghanistan before the end of this week, the Yonhap news agency quoted a Taliban spokesman as saying.

The crisis began on July 19 when 23 Korean church members, who were said to be there to help in schools and hospitals rather than as missionaries, were taken captive when travelling by bus between Kabul and the southeastern city of Kandahar.

The militants said it would release the hostages only in return for Taliban fighters jailed by the Afghan government - a condition that the Korean government repeatedly said it did not have the ability to meet.

In a demonstration of its seriousness, the Taliban killed two male hostages in the early days of the crisis, although two women were later released as a "gesture of goodwill".

However, there was some confusion surrounding Tuesday's deal. Seoul had already agreed to pull its army units out of Afghanistan by the end of the year and imposed a complete ban on travel to the country following the seizure of the hostages.

Korean media had previously reported that the Taliban were seeking payment for the return of the hostages but there was no word on Tuesday of any money changing hands.

The families of the hostages, who have been gathered for the last six weeks at the Saemmul Church in the commuter town of Bundang, south of Seoul, were overwhelmed by Tuesday night's news, crying and rejoicing in equal measure.

Korea as a nation has similarly run the gamut of emotions since the hostage crisis began. After the initial period of shock, during which there were large demonstrations calling for the hostages' safe return even if it meant paying money to the captors, there was widespread anger at the missionaries' defiance of travel warnings against going to such a dangerous country.

But in the last two weeks the sense of crisis has significantly lessened, as the Korean government sought to calm the situation and create a suitable climate for a low-key deal to be reached without endangering more lives.