NAIROBI, Kenya-- Ten heavily armed Somali militants driving their boat under the cover of darkness kidnapped a Frenchwoman on a resort island in northern Kenya early Saturday, officials said. The woman often uses a wheelchair, according to the resident.

The government blamed the attack on Somali militants from al-Shabab, and Kenyan navy and police chased the suspected boat at sea.

"Security forces swung into immediate action and pursued the abductors as they sped northwards in a high-speed boat towards" Ras Komboni, the town in Somalia the government said the militants originated, according to a government statement.

"In the ensuing shoot-out between the abductors and the Kenya Navy, several of the abductors were injured but managed to enter" Ras Komboni, the statement said.

At one point during the chase two Kenyan boats had the suspected pirate boat surrounded, with four men and the kidnapped woman on board, said Tourism Minister Najib Balala. A plane overhead was also monitoring the situation, he said.

"We are just concerned about the safety of the lady," said Balala. He identified her as Marie Dedieu. French officials said in a statement that she is in her 60s. The Kenyan government called her "elderly" and one official said she was in her 70s.

Ambrose Munyasia, a top police official on the coast, said he had information that the French government would join the chase. He said he was optimistic the woman would be rescued soon.

But by early evening in Kenya there was no news of a successful rescue. In a message to Kenyans, the government said that "adequate security measures" had been put into place.

The French Foreign Ministry said in a statement that French officials are "working with the Kenyan authorities, who have mobilized significant air and sea resources in order to free our compatriot."

Officials had earlier indicated Somali pirates had pulled off the attack, before the government later blamed al-Shabab. If pirates are involved, it would be the second such attack near the popular tourist town of Lamu in a month. In early September, pirates shot dead a British man and kidnapped his wife from a resort near Lamu.

People near the scene of the kidnapping heard gunshots around 3 a.m., Lamu resident Muhidin Athman said. Athman said the Frenchwoman owns a house on Manda Island and lives there half the year. She gets around with the help of a wheelchair or personal assistants, Athman said.

Manda Island is just across the channel from Lamu, an old resort town. Two kidnappings within a month have the potential to greatly harm the tourist trade in the area just before the busy holiday season.

After the attack, the French Foreign Ministry updated its travel advice for Kenya, "formally discouraging" trips to the Lamu archipelago and the surrounding area.

Pirates once focused primarily on big ships at sea, but in recent years have also attacked private yachts, capturing Europeans or Americans on private trips.

As U.S. and European navies have increased their patrols of the Indian Ocean, and as large ships have increased their on-board defenses, pirates may be looking for easier targets to keep ransom payments coming in.

Pirates kidnapped and held a British couple -- the Chandlers -- for more than a year.

"It's profit-motived action. As we know the British couple we captured before paid huge ransoms, so sometimes these targets are a big gain that gives you more than ships," a man who identified himself as a pirate commander named Bile Hussein told The Associated Press last week.