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A French woman has been kidnapped by an armed gang on Kenya's northern resort island of Manda and taken to Somalia, Kenyan officials say.

The disabled woman, 66, was attacked at her bungalow at Ras Kitau. Kenya's government said it believed the abductors were al-Shabab militants.

A Kenyan statement said some abductors were injured in a shootout with two Kenyan ships trying to stop them.

The kidnap comes three weeks after a UK couple were attacked further north.

Gunmen shot dead husband David Tebbutt and kidnapped his wife Judith in Kiwayu. She was taken across the border to Somalia.

The gunmen struck at Ras Kitau at 03:30 (00:30 GMT) on Saturday.

"An elderly, disabled French lady who has been living in Manda Island in her own house was abducted by 10 heavily armed Somali bandits suspected to be al-Shabab operatives from Ras Chiamboni in Somalia, near the Kenyan border," a Kenyan government statement said.

Abu Chiaba, a local legislator, said the gang had come into Manda by boat in the middle of the night.

"The elderly French woman is well known in the area, she comes to Manda regularly," Mr Chiaba said.

Witnesses say they heard at least two gunshots before the woman was taken away by the attackers.

"We were all startled awake because there were gunshots," said Jeremiah Kiptoon, who works on Manda island.

"The dogs were barking and people were screaming... I ran to the place to see what was happening but by the time I got there, the lady was gone."

Two coastguard vessels and a police helicopter chased the abductors, and were involved in an exchange of fire, Internal Security Minister George Saitoti said in a statement.

He said several of the abductors were injured but they still managed to enter Somali territory in a motor boat.

The government said "every effort" was being made to rescue the woman.

Kenya's Tourism Minister Najib Balala called for international assistance to help them in their efforts to secure the border with Somalia.

"The core problem is Somalia and the core problem is criminal elements who manage to sneak into the country," he told the ³ÉÈË¿ìÊÖ.

"Whatever we're going to do, if we don't have the support of the international community to address the Somali issue then it is very challenging to manage to man the border in Somalia."

France has warned French visitors to avoid the area.

"It is advised against staying on the Lamu archipelago and its region near the Somali border," the French foreign ministry said on its website.

The attack happened just across a lagoon from Shela - an exclusive resort on Lamu island.

This attack has the potential to do severe damage to Kenya's tourism industry, the ³ÉÈË¿ìÊÖ's Will Ross in Nairobi says.