"I am safe and unharmed. We would like to appeal for a safe negotiation."
The government has refused to bargain with hostage-takers and instead has begun an operation to find the hostages, sending troops down to a remote southern island after gunmen were reportedly spotted there.
But one hostage - an American missionary - has appealed to the government on local radio to negotiate for his release.
"Hi, I am Mr Martin Burnham, a US citizen. I am a missionary. I am with my wife, we are in the custody of the Abu Sayyaf," he said in a telephone interview.
"I am safe and unharmed. We would like to appeal for a safe negotiation."
Mr Burham's wife and another US citizen were among the group seized from the Dos Palmas resort off the western Philippine island of Palawan on Sunday.
The Abu Sayyaf were behind a series of high-profile kidnappings of foreign tourists last year.
The hostages were eventually released after mediation by a Libyan representative and the reported payment of a large ransom.
Sighting reported
A military spokesman said the mayor of the island town of Mapun, in the south-western Tawi-Tawi archipelago, had alerted the authorities about sighting gunmen.
The rebels have reportedly split the hostages into three groups and taken the groups to different places.
Philippines President Gloria Arroyo has spelt out her refusal to negotiate.
"We will not allow a repeat of last year where ransom was paid. No ransom, no negotiation," her national security advisor Roilo Golez said.
Most of those seized from Palawan were ethnic Chinese Filipino tourists while the other American hostage was Guillermo Sobero from California.
The gunmen, who arrived on two boats, also took away four resort staff.
The Burnhams, missionaries from the state of Kansas, were celebrating their 18th wedding anniversary at the Dos Palmas resort.
The US State Department issued a statement urging Americans to be careful when travelling in the Philippines and to avoid certain islands.
Kidnapping common
BBC South East Asia correspondent Jonathan Head says kidnapping is a common crime in the Philippines, especially among the Islamic separatist rebels in the south.
But he says the motives vary, often mixing political objectives with demands for large ransoms.
Police said all other tourist resorts on Palawan had been put on alert and navy ships had stepped up security around the island.
Armed forces chief Diomedio Villanueva has gone to the region to supervise the military response to the kidnapping.
He would not say whether the attackers were from Abu Sayyaf.
Mrs Arroyo has offered to make peace with the largest Muslim group in the south, but she has ruled out any deal with Abu Sayyaf.