The Philippines on Monday condemned the "barbaric beheading" of a German captive by the Abu Sayyaf militants, who posted a video of the killing after a deadline for a $600,000 ransom passed.

The video showed a machete-wielding militant behead the elderly German hostage, Jurgen Kantner, who had appealed for help twice in short video messages, saying he would be killed if ransom was not paid.

Jesus Dureza, presidential adviser on the Philippine peace process, said officials had exhausted all efforts to save Kantner, who was held on the tiny southern island of Jolo, but to no avail.

"We grieve as we strongly condemn the barbaric beheading of yet another kidnap victim," Dureza said in a statement.

"...Terrorism has no place in a country like ours and we as a people must confront violent extremism every time it rears its ugly head. There must be a stop to this killing of the innocent and the helpless."

He did not mention the demand for ransom.

Kantner and his companion were taken captive in November while sailing on a 53-footer yacht near Sabah, eastern Malaysia, and brought to Jolo. His companion was shot dead when she tried to resist the militants.

Last year, Abu Sayyaf beheaded two Canadians on Jolo but their two companions, a Filipino woman and a Norwegian, were freed.

The group has made tens of millions of dollars from ransom money since it was formed in the 1990s, security experts say, channelling it into guns, grenade launchers, high-powered boats and modern equipment.

Abu Sayyaf is believed to be holding 26 hostages - 13 Vietnamese, seven Filipinos, a Dutch national, a Japanese, two Indonesians and two Malaysians. They have freed several others in return for ransom payments.