The kidnapped staff include Eugenio Vagni, 62, of Italy, Andreas Notter, 38, a Swiss and Mary Jean Lacaba, 37, a Filipino.
The threat to behead one of the hostages was made by Albader Parad, Abu Sayyaf's leader, who has given the government until March 31 to withdraw.
Marga Ortigas, Al Jazeera's correspondent in Manila, said that although the government is facing pressure to consider the demands of the Muslim group, it does not mean they are "conceding to Abu Sayyaf's demands".
"According to the interior secretary, they are willing to move troops from certain key areas that the Abu Sayyaf have asked them to vacate ... to give them breathing space so that they might effect the release of one hostage," she said.
Puno said up to 600 to 800 police and pro-government forces would pull back to allow the kidnappers to release them.
"I think we are more than bending over backwards in order that the kidnappers will not feel threatened," he said.
|Abu Sayyaf has kidnapped a number of foreigners and locals in the past [Reuters]
Yasser Igasan, an Abu Sayyaf official, told Al Jazeera by telephone: "The hostages are all OK. They're still here, very much alive. But they are very scared because of the ultimatum.
"If the military does not pull out, we will behead one of them."
Igasan said the pullout does not guarantee the hostages' release, but it would open the way for further negotiations.
He said the Abu Sayyaf had not asked for a ransom, and the group had political demands concerning a separate Muslim homeland that they would only talk about if the troops withdrew.
"We have objectives that are not just for us, but for all Muslims," Igasan said.
Alain Aeschlimann, the Asia-Pacific operations chief for the ICRC, said they had been in contact with the hostages on Monday, and that the beheading threat "has obviously increased the stress and hardship they are experiencing".
"Following the kidnappers' renewed threats, the ICRC once again appeals to the abductors' sense of humanity and asks them to avoid taking any action that could endanger the lives of Mary Jean, Eugenio and Andreas," he said.
Aeschlimann also called on Philippine authorities to "refrain from further military operations in the area" as it could put the hostages at risk.
But the government seemed reluctant to heed his appeal.
Abu Sayyaf have kidnapped a number of foreigners and locals in the past.
Five people have already died in clashes between the kidnappers and the military trying to hunt them down.