A gang of militant gunmen who kidnapped a Frenchwoman in Kenyan territory have evaded Kenyan naval forces and escaped to Somalia.

Kenyan officials say the militants landed on Kenya's Manda Island under cover of darkness early Saturday. They stormed the woman's beach house in a hail of gunfire that terrified neighbors. The militants then carried the victim off to their boat and tried to flee while Kenyan boats and aircraft gave chase.

A Kenyan government statement late Saturday said some of the gunmen were injured during an exchange of gunfire but that they still managed to escape across the border to Ras Komboni in Somalia.

Kenyan officials say they suspect the gunmen are aligned with al-Shabab, a group linked to al-Qaida that controls large portions of southern Somalia. The gunmen earlier had been described as pirates.

Kenyan police spokesman Charles Owino identified the kidnapped woman as Marie Dedieu, a French national in her 60s. Dedieu's neighbors say she is only able to get around with the help of a wheelchair or her personal assistants.

Kenyan police say they will be increasing security along the coastline as a result of this latest incident.

Saturday's kidnapping took place across a lagoon from Lamu island, a popular Kenyan resort near where pirates kidnapped a British woman earlier this month and shot her husband to death.

Pirates have brought in millions of dollars in ransom for several years by attacking large ships, but in recent years, they have also attacked smaller targets such as private yachts. The attacks continue, even as U.S. and European navy patrols increase.