"We had a telephone contact with the South Korean side today (Saturday) and the South Korean side asked to give two days," Abdullah Jan, a Taliban commander, was quoted by Yonhap as saying in a telephone interview with the agency.
The Taliban kidnapped 23 South Koreans on July 19, when they were traveling by bus from Kabul to Kandahar on a humanitarian mission.
Taliban militants have already executed two men and threatened to kill others, many of whom are women, if the South Korean military contingent does not leave Afghanistan and the Afghan government does not release its imprisoned fighters.
Following the first round of negotiations with South Korea, Taliban released two seriously ill women hostages Monday. The negotiations resumed Thursday.
Meanwhile, Taliban spokesman Qari Yousuf Ahmadi said Saturday that the militant group would kill one or two hostages, if South Korean negotiators were not "as active in negotiations" as they were in the past, according to Yonhap.