A mother of one of the South Korean hostages in Afghanistan cries during a news conference calling for their safe return, in Sungnam, South Korea. South Korean families pleaded Tuesday for help from the United States to peacefully resolve a hostage standoff in Afghanistan as they mourned the death of a second captive amid fears that rejecting the Taliban captors' demand for prisoner releases could lead to more killings.

Ghazni, Afghanistan ? South Korea and relatives of 21 kidnapped Koreans appealed for U.S. help Tuesday, but Afghanistan said for the first time it will not release insurgent prisoners – the Taliban’s key demand to free the captives.

Afghan police found the body of the second hostage slain since the Christian church group was seized nearly two weeks ago; the group’s pastor was killed last week.

A purported Taliban spokesman, meanwhile, said some of the prisoners the militants want released are held at the U.S. base at Bagram – and the Al-Jazeera television network broadcast a video Tuesday reportedly of another Taliban captive, a German engineer.

The Taliban said more Koreans will die if its demands are not met by midday today. The militants have extended several previous deadlines without consequences, but killed 29-year-old Shim Sung-min on Monday after a deadline passed. His body, with a gunshot wound to the head, was found along a road in Andar district.

They were two of 23 South Koreans – 16 women and seven men – kidnapped while riding a bus July 19 on the Kabul-Kandahar highway. They are the largest group of foreign hostages taken in Afghanistan since the 2001 U.S.-led invasion that drove the Taliban from power.

In South Korea, relatives and a civic group pleaded for more U.S. involvement, and the president’s office used more diplomatic language to prod the Americans.

“The government is well aware of how the international community deals with these kinds of abduction cases,” the president’s office said, an apparent reference to the U.S. policy of not negotiating with terrorists. “But it also believes that it would be worthwhile to use flexibility in the cause of saving the precious lives of those still in captivity.”

The civic group People’s Solidarity for Participatory Democracy questioned what South Korea had earned for helping Washington combat terrorism. Seoul has sent troops to Afghanistan and Iraq.

State Department spokesman Tom Casey said there is regular contact between U.S. and South Korean officials on the standoff.

President Hamid Karzai’s spokesman said officials were doing “everything we can” to secure the hostages’ release, but that freeing militant prisoners was not an option.

“As a principle, we shouldn’t encourage kidnapping by accepting their demands,” said Humayun Hamidzada.