KUALA LUMPUR (Reuters) - The Philippines on Thursday agreed to allow Malaysia and Indonesia to carry out "hot pursuits" in its territorial waters, as the three nations look to tackle kidnappings and piracy by Islamist Abu Sayyaf rebels.

The announcement was made by Prime Minister Najib Razak after a meeting with Philippine President Rodrigo Duterte, who is on a two-day visit to Malaysia.

"When we reach their waters, they have allowed us to keep chasing these kidnap-for-ransom groups," Najib said at a news conference.

He said the agreement would be further discussed at a meeting between the three countries on Nov 22 in Vientiane.

Abu Sayyaf rebels have been intercepting slow-moving tugboats in waters near the borders of Malaysia and the Philippines, taking captive more than a dozen Indonesian and Malaysian sailors.

Several hostages have been freed, after paying ransom to the Abu Sayyaf, a group linked to al-Qaeda and known for kidnappings and beheadings, including of two Canadians this year.

On Monday, the Philippine military said a German national was believed to be the latest person to be taken hostage. His companion, a woman, was found dead on a yacht abandoned on a remote island in the Sulu archipelago, an Abu Sayyaf stronghold.

The Abu Sayyaf is holding another 15 captives, including a Netherlands citizen, five Malaysians, two Indonesians and seven Filipinos.

(Reporting by Rozanna Latiff; Editing by Nick Macfie)