The Philippines and Germany are condemning the beheading of an elderly German captive by Islamic State-linked Abu Sayyaf militants who posted a video of the killing after a deadline for a $US600,000 ($A781,140) ransom passed.
The video showed a machete-wielding militant behead Jurgen Kantner.
The German had appealed for help twice in short video messages, saying he would be killed if ransom were not paid.
On Monday, Jesus Dureza, presidential adviser on the Philippine peace process, said officials had exhausted all efforts to save Kantner, 70, who was held on the tiny southern island of Jolo.
He made no mention of the ransom demand.
The Philippines' armed forces pledged in a separate statement to bring Kantner's killers to justice and to continue operations to free other hostages held by Abu Sayyaf.
In Berlin, Chancellor Angela Merkel called for a united international front against terrorism.
"The chancellor condemns this hideous attack that shows, once again, how unprincipled and barbarous terrorists act," her spokesman Steffen Seibert said.
Last year Abu Sayyaf decapitated two Canadians on Jolo but later freed their two companions, a Filipino woman and a Norwegian. The four had been seized from a tourist resort. The ransom demand for the Canadians was $US6.4 million each.
Abu Sayyaf's activities in recent years have been mainly banditry, but the Philippines believes Islamic State has been in contact with members of the group's leadership with a view to gaining a foothold in Southeast Asia.
Kantner and his companion were taken captive in November while sailing near Sabah, eastern Malaysia, and brought to Jolo. His companion was shot dead when she tried to resist the militants.
Reports of Kantner's execution emerged on Sunday evening, but the military only confirmed the killing on Monday, citing "reliable sources".
Abu Sayyaf is currently holding 26 hostages - 13 Vietnamese, seven Filipinos, a Dutch national, a Japanese, two Indonesians and two Malaysians, the military said.
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