A disabled Frenchwoman who was snatched by gunmen from her beachfront home at a Kenyan resort and taken to neighbouring Somalia has died in the hands of her captors.

The foreign ministry said the circumstances of 66-year-old Marie Dedieu's death were not known, but her failing health had probably been a factor.

"This was an act of unqualified barbarism, violence and brutality," foreign minister Alain Juppe told reporters.

"We condemn this in the strongest possible terms. We did everything possible to try to obtain her release, we tried to send medication by numerous different channels and apparently these savages could not care less."

The announcement of her death came as Kenyan jets pounded the positions in Somalia of Al Qaeda-linked Al Shebaab militants, whom Kenya blames for a spate of abductions of foreigners.

Kenyan forces launched an unprecedented incursion, which it says has already killed dozens of Al Shebaab fighters, into Somalia this week with the blessing of the Western-backed government in Mogadishu.

A gang of 10 armed men seized Ms Dedieu from Manda Island in Kenya's Lamu archipelago earlier this month and fled by sea to Somalia, fighting off an attempt by Kenya's navy to stop them.

There had been serious concern over the health of Ms Dedieu, who was wheelchair-bound after an accident several years ago, recovering from cancer and required medication every few hours.

The foreign ministry said it had informed Dedieu's family of her death and had demanded the unconditional return of her remains.

Kenyan officials said they suspected Somali Islamist Al Shebaab insurgents had carried out the abduction, but the militants denied the charge.

Ms Dedieu had lived for 15 years in the Lamu archipelago, off Kenya's northern coast, in a traditional Swahili-style house with a thatched roof a few metres from the sea.

She was a well-loved local figure and residents were in shock at the news of her death.

Ms Dedieu's kidnapping was the second in the area in less than a month and dealt a blow to Kenya's tourist trade after European governments warned travellers to avoid the Kenyan coastline near Somalia.

A British tourist was seized to the north of Lamu and taken to Somalia on September 11 by an armed gang who killed her husband. She is believed to have been sold to pirates now holding her in central Somalia.

A third incident, the kidnapping of two Spanish aid workers at the Dadaab refugee camp, took place last Thursday and apparently prompted the Kenyan incursion into Somalia.

AFP