The Afghan and US presidents ruled out making any concessions to Taliban militants holding 21 South Koreans, as Afghan doctors sent medicine to some of the sick captives held for three weeks.
Qari Yousef Ahmadi, who claims to speak for the Taliban, said the lives of the hostages rest in the hands of Afghan President Hamid Karzai and US President George W Bush, who are meeting at Camp David in the US state of Maryland.
He also warned that the Taliban would still kidnap foreigners if the government refuses to meet their demand to exchange the South Koreans for militant prisoners.
Two of the hostages seized three weeks ago are said to be extremely sick, and an Afghan doctor who heads a private clinic said he had dropped off almost US$2,000 (euro1,450) worth of antibiotics, vitamins and first aid kits in rural Ghazni province on Sunday intended for the captives.
Dr Mohammad Hashim Wahwaj said the Taliban told him that they had picked up the medicine.
The Taliban kidnapped 23 South Koreans from a church group on July 19 as they traveled by bus from Kabul to Kandahar to work on medical and other aid projects. The Taliban have executed two men and threatened to kill others, including 16 women, if the Afghan government doesn't release its fighters in custody. In South Korea, the husband of one of the hostages posted a video message on YouTube on Monday, telling his wife not to give up hope because they will see each other soon.
The Taliban have demanded that 23 militant prisoners being held by Afghanistan and at the US military base at Bagram be freed in return for the Koreans, but the Afghan government has all but ruled that option out.
The subject was also discussed during a meeting between Karzai and Bush at Camp David, and the two leaders agreed that "there should be no quid pro quo" that could embolden the Taliban, said Gordon Johndroe, a Bush spokesman.
A South Korean presidential spokesman had cautioned against expecting too much from the summit.
"It is our government's standpoint that we should work separately from the summit to resolve the hostage issue. It is inappropriate to have any premature expectations or to overly interpret the summit," Cheon Ho-sun said in Seoul. South Korea has asked Kabul to be flexible in its policy of non-negotiation with terrorists.
Ahmadi said the militants and South Korean officials remain in contact over the phone, but have not yet agreed on a location where they can hold negotiations over the fate of the captives. In Seoul, an official said on Monday that South Korean diplomats had made contact with the captives. The official, who spoke on condition of anonymity because of the sensitivity of the issue, declined to give further details about the conversation with at least one of the captives.