Julasirim Kasim, the provincial police chief, on Thursday said government forces were "sealing off" areas where the gunmen and the Italian, Swiss and Filipino hostages were sighted.
"We continue to hope that the worst did not happen and will not happen"
Alain Aeschlimann, ICRC regional operations chief
He said police were continuing to set up road checkpoints around Jolo.
The three Red Cross workers – Italian Eugenio Vagni, Swiss Andreas Notter and Filipino Mary Jean Lacaba – have been in captivity since January 15.
They were kidnapped while heading to a local airport after visiting a Red Cross water sanitation project at the provincial jail.
In a statement posted on the International Committee of the Red Cross website, Alain Aeschlimann, the regional operations chief, confirmed there was no news on the hostages' fate.
|Switzerland, Italy and Pope Benedict XIV have appealed for the hostages' release [Reuters]
"We continue to hope that the worst did not happen and will not happen," he said in the posted interview.
"We have taken note of reports that the kidnappers' threat was not carried out."
Earlier in the week, Abdusakur Tan, the governor of southern Sulu province, said the group and the hostages were on the run as the government redeployed troops around a hilly area on the island close to their camp.
Tan had declared a state of emergency on Tuesday, hours after the beaheading deadline set by the militants lapsed.
The Abu Sayyaf has beheaded hostages in the past, including an American in 2001 as well as seven Filipinos in 2007.
Other officials said intermediaries had established contact with the kidnappers, but no details have been made immediately available.
The Swiss government has appealed to the kidnappers to "show compassion" and release the captives.
"[They] have dedicated their lives to the cause of peace and to helping the most disadvantaged people in the world," a statement said.
The Italian government, and Pope Benedict XVI, the head of the Roman Catholic church, also appealed to the Abu Sayyaf group to spare the lives of the hostages.
The Abu Sayyaf, which is also said to have links to the regional Jemaah Islamiyah, has been blamed for the worst attack in the Philippines' history, in which a ferry in Manila Bay was bombed in 2004, killing 100 people.
The US government has placed the group, which has about 400 armed men, on its list of terrorist organisations.