Taliban leaders and South Korean officials negotiated by phone over the fate of 19 remaining hostages, but no new face-to-face talks had been planned, the International Committee of the Red Cross said Tuesday.

Two Korean women were released Monday in the first breakthrough in a drama that began more than three weeks ago when a busload of 23 South Korean church volunteers was seized. Two of the hostages, both men, were killed last month.

The handover came after two days of face-to-face talks between the Taliban and a South Korean delegation. Franz Rauchenstein, an official with the International Committee of the Red Cross said, officials were ready to host more talks at the office of the Afghan Red Crescent in Ghazni, but the two sides were talking by phone for now.

"We stand ready to play the role of neutral intermediary for the release of the next 19 hostages and we are urging the two parties to make it a short process in the interest of the hostages," he said.

The South Korean Embassy said the two women were transferred taken from the U.S. base at Ghazni to a safe place in "our care," and that they were in good condition and awaiting a flight home "very soon."

"They got medical checks, and nothing serious happened," said an embassy official, who spoke on condition of anonymity because of embassy policy.

It was likely that the women were flown to the U.S. base at Bagram, where the South Korean military runs a hospital.

The official said South Korean delegates in Ghazni were "still maintaining negotiation channels" with the Taliban leaders but declined to give further details.

A Taliban spokesman said they released the women as a show of goodwill because negotiations were going well. Qari Yousef Ahmadi also reiterated the militants' demand that Taliban prisoners be released in exchange for the remaining 19 hostages.

Ghazni Gov. Marajudin Pathan, who in the past has suggested the hostage standoff could be solved with a ransom payment, ruled out a prisoner swap.

ICRC officials waited for the Koreans on a stretch of desert road 5 miles south of the city of Ghazni. When a dark gray Toyota Corolla stopped, two women got out of the back seat and began crying at the sight of the waiting Red Cross SUVs.

The South Korean Foreign Ministry identified the freed hostages as Kim Kyung-ja and Kim Ji-na. Previous media reports said they were 37 and 32 years old, respectively.

Meanwhile, Iranian President Mahmoud Ahmedinejad made his first-ever visit to Afghanistan, calling Iran's eastern neighbor a "brotherly nation" whose stability is paramount for the region.