Philippine President Rodrigo Duterte interacts with reporters during a news conference upon his arrival from a four-day state visit in China at the Davao International Airport in Davao city. Thomson Reuters MANILA (Reuters) - Philippine President Rodrigo Duterte warned on Wednesday he might "invade" an island stronghold of the Islamic State-linked Abu Sayyaf to "finish the game" following a thwarted attempt by the group to kidnap tourists on a resort island last week.

Duterte offered cash rewards for the capture, dead or alive, of six Abu Sayyaf militants still at large following a day-long clash last week on Bohol island, which killed six rebels and four members of the security forces.

The shootout on Bohol followed warnings against travel to central Philippine islands by several Western countries, which cited unconfirmed intelligence of possible kidnap plans. The clash erupted after residents tipped-off authorities about the arrival of armed men on boats.

The incident was highly significant, coming during Holy Week at a location far from Abu Sayyaf's traditional field of operations on remote Jolo, Tawi Tawi and Basilan islands.

Duterte said Abu Sayyaf must not be allowed to extend its reach.

"I will, maybe, invade Jolo," Duterte told reporters after a security briefing in Tagbilaran City, Bohol.

"All army, navy, will go there. It will be a fight. That's what they want, I will give it."

Referring to Abu Sayyaf's strongholds, he said: "They must stay there, My order to the navy ... is to blow them up, no surrender. Shoot cannons, destroy them."

Duterte lights a candle at the blast site in front old Davao International Airport terminal in 2009 to commemorate the 6th anniversary of a bombing incident claimed by Abu Sayyaf that killed 22 persons and injured135 others. Keith Bacongco/AKP Images

Abu Sayyaf has its roots in separatism and the military says some elements are in close contact with Islamic State radicals in the Middle East. However, most of its activities are banditry, like piracy and kidnap. It is notorious for beheading hostages when money for their release is not paid.

Duterte said he wanted civilians to support the manhunt on Bohol and offered a reward of 6 million pesos ($120,668) for each of the six fugitives.

He warned Abu Sayyaf might try to "create a disaster" at an meeting of trade officials of the Association of South East Asian Nations (ASEAN).

Duterte said he wanted to arm civilians, and encouraged them to kill not only Abu Sayyaf, but drug addicts who were armed.

Duterte's signature policy is a war on drugs, which has killed nearly 9,000 people in 10 months, mostly users and small-time peddlers.

"My order is dead or alive ... My enemy is drugs and terrorists. These drug addicts, they have firearms. Almost all of them are really paranoid. They fight."