Islamist militants have killed a German sailor and abducted her elderly husband from a yacht in the southern Philippines, according to the military.

The victims, who have not been formally identified, are believed to be Sabine Merz and 70-year-old Jurgen Kantner, the same couple who were abducted by Somali pirates and held hostage for 58 days off the Gulf of Aden in 2008.

A Commander from Abu Sayyaf, a group known for kidnapping foreigners and beheading them when ransom demands are not met, has claimed responsibility for the most recent incident.

Military spokesman Filemon Tan said the military had found the couple’s yacht with the body of a naked woman aboard matching Ms Merz's description, who had been shot.

In an audio recording heard by the military, the abducted man identified himself as Mr Kantner, and named his companion as Sabine.

In a 2009 interview with news agency AFP, Mr Kantner said he would never stop sailing despite having been subjected to a mock execution during the pair's first kidnapping ordeal in 2008.

"My boat is my life and I don't want to lose her, nothing more. I don't care about pirates and governments," he said from Berbera, the main port in Somaliland.

The Philippine military released a photo on Monday of the Rockall yacht and said it had a German flag on it.

Philippine military released a photo of the couple's yacht, Rockall (Philippine military)

Mr Tan confirmed the passports of both Ms Merz and Mr Kantner were found aboard and the photo in Ms Merz’s passport appeared to match the body of the woman found dead.

Abu Sayyaf has defied more than a decade of US-backed military offensives to diminish its capacity to carry out lucrative kidnappings in the region.

In 2014, the group abducted another German couple from a yacht in the southern Philippines. The pair were released six months later after receiving what they said was the full ransom demand of 250 million pesos ($5.1 million).