Police said all other tourist resorts on Palawan had been put on alert and navy ships had stepped up security around the island.
A presidential spokesman said police had sighted the gunmen and were "very confident that the kidnappers could be encircled and hostages released".
Most of those seized were ethnic Chinese Filipino tourists but there were also three Americans, identified as Martin and Gracia Burnham, missionaries from the state of Kansas, and Guillermo Sobero.
The gunmen, who arrived on two boats, also took away four resort staff.
"We have our helicopters and aeroplanes with reconnaissance capabilities. We also have patrol boats going in that direction to cut them off," Captain Djo Jalandoni of the military's western command said.
President Gloria Arroyo ruled out any negotiations with the gunmen for ransom money.
The 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.
Tourist targets
On Tuesday an armed group attacked another resort on the southern island of Mindanao, killing two local staff. None of the guests was harmed then.
Police said all other tourist resorts on Palawan had been put on alert and navy ships had stepped up security around the island.
The Abu Sayyaf rebel group seized 40 people in a series of raids in the southern Philippines and a nearby Malaysian resort last year, holding some for many months.
They were eventually released after mediation by a Libyan representative and the reported payment of a large ransom.
Armed forces chief Diomedio Villanueva would not say whether the attackers were from Abu Sayyaf, which is based on the southern island of Jolo.
President Gloria Arroyo has offered to make peace with the largest Muslim group in the south, but she has ruled out any deal with Abu Sayyaf.