"We have extended the deadline and now the final deadline is 10am (0530 GMT)," Akbar Agha, commander of Jaish al-Muslimin (Army of Muslims), told the Afghan Islamic Press on Thursday.
Agha told the private Pakistan-based news agency that the Afghan government had made contact with the group late on Wednesday before a midnight deadline.
He was hopeful that negotiations would begin on Thursday. The new Taliban splinter group has demanded the US release all Taliban prisoners and that foreign forces and the United Nations quit Afghanistan.
Agha on Wednesday had accused the government of trying to buy time by appearing to negotiate.
"I am not satisfied with the negotiations. I believe the government is trying to gain time to rescue the hostages," he was quoted as saying by AIP.
But a spokesman for the group said that talks were imminent. "The Afghan government and the UN agreed to negotiations with us ... and talks will be started," Sayid Khalid Agha said on Thursday.
The three captives - Annetta Flanigan from northern Ireland, Shqipe Habibi from Serbia's mainly Muslim province of Kosovo, and Angelito Nayan from the Philippines - were seized at gunpoint on 28 October from their vehicle in busy lunchtime traffic in Kabul.
The hostages' jobs were to
oversee Afghanistan's elections
They had been helping to oversee Afghanistan's first presidential election. The Afghan government on Wednesday night appealed to the public to phone in with any information they might have on the captors or their captives.
"We have put in place a hotline and we want cooperation from the people," interior ministry spokesman Lutf Allah Mashal said.
Mashal had earlier expressed optimism at winning the release of the three election workers, whose snatching has cast a pall over the otherwise peaceful 9 October elections.
US-backed incumbent Hamid Karzai was officially declared the winner on Wednesday.
The captors said on Tuesday they had given UN mediators a list of Taliban prisoners held in Afghanistan.
The Nato-led International Security Assistance Force, a 9000-strong peacekeeping force, offered to help rescue the captives or secure their release.
Meanwhile, two improvised bombs exploded near US and
Swedish aid agency offices in Afghanistan's restive east but no one was injured, a US military spokesman said on Thursday.
The two home-made bombs exploded around 9pm on Wednesday in the eastern city of Jalalabad near compounds housing USAID, Washington's overseas aid wing, and the Swedish Committee for Afghanistan, US Major Mark McCann said.
"There were no injuries," he said.