Mulla Sabir Mumin, one of several men claiming to speak for Jaish-e Muslimin (Army of Muslims), said on Sunday the talks with UN and government negotiators were taking place by telephone.
"We have backed away from some of our demands," he told reporters, without elaborating. "Our talks are going on directly and over the phone. We are hopeful of a successful end."
The kidnappers have threatened to kill Filipino Angelito Nayan, Annetta Flanigan from Northern Ireland and Kosovan woman Shqipe Hebibi unless their demands - including the release of Taliban prisoners, the withdrawal of US troops and the suspension of UN operations in the country - are met.
Meanwhile, a relative of one of the hostages has made a televised appeal for her release, saying she is a Muslim who came to help Afghanistan.
Pakdi Behgjet made the appeal on behalf of Kosovar hostage Shqipe Hebibi on the private Afghan television channel, Toloo.
"Please take care of Shqipe Hebibi, you know that she is a Muslim, she comes from a poor family, she comes from a poor country"
Relative of Shqipe Hebibi
"Shqipe Hebibi went to Afghanistan to help our brother people here," he said. "Please release her, we are waiting every day.
"Please take care of Shqipe Hebibi, you know that she is a Muslim, she comes from a poor family, she comes from a poor country," he said. Behgjet was described only as a relative of Hebibi.