Kenyan jets struck in Somalia Wednesday in a bid to rid the border area of Islamist rebels blamed for a spate of abductions, including that of a French woman who died in captivity, officials said.

Kenyan ground troops guided by pro-government Somali forces prepared for a fresh assault against the Shebab insurgents with the blessing of the Western-backed government in Mogadishu and its Ugandan protectors.

Nairobi's unprecedented military incursion into Somalia, which it said had already killed dozens of Shebab fighters, triggered dire warnings by a top Shebab leader of bloody retaliation.

The foreign ministry in Paris announced the death of Marie Dedieu, a 66-year-old wheelchair-bound woman snatched from her beach house in the Kenyan resort of Lamu earlier this month and taken to Somalia by her kidnappers.

"Our aircraft are involved in the operations," army spokesman Major Emmanuel Chirchir said, on the fourth day since Kenya declared war on the Shebab militia.

Heavy air strikes are reported to have been hitting Shebab positions in efforts to dislodge the militants, before Kenyan-backed Somali government ground troops move in to drive out rebels, according to witnesses.

Analysts say Kenya wants to carve out a buffer zone along the border, but Shebab forces said Wednesday they were preparing a counter-attack.

"We have been gathering information on the Kenyan army's strength, in terms of weapons and manpower," Sheikh Abdulaziz Abu Musab, a Shebab spokesman, said on the group's radio Al-Andalus.

The main forward base of Kenyan operations is at Qoqani, some 100 kilometres (60 miles) from the border, as they prepare to push forward to seize Afmadow, which Somali government forces are already fighting to secure.

"In terms of injuries, the first attack saw the death of 73 Shebab," Chirchir said, adding that the only Kenyan deaths were five killed in a helicopter crash.

A Kenyan police source however told AFP there were casualties.

Kenya's shock assault against the hardline Shebab has sparked a fierce reaction with the militants warning of reprisals on "all fronts."

Security forces are planning a "major operation in Nairobi to get rid of Al-Shebab," Assistant Security Minister Orwa Ojode said Wednesday, a rare admission from the government the Shebab threat exists even in the capital.

The Shebab deny any involvement in the recent kidnapping of foreigners, which have raised questions about Kenya's ability to host the million tourists who visit each year and one of the world's largest aid communities.

Kenya's decision to invade came after a British tourist was snatched from a Kenyan resort last month, the French woman from her beachfront home in Lamu and two Spanish aid workers from Dadaab refugee camp last week.

A French government statement said "the conditions of her detention and the fact that the kidnappers probably refused to give her the medication that we sent her" likely led to her death.

Insecurity in southern Somalia is making it "almost impossible to establish significant cross border humanitarian operations," the UN humanitarian affairs agency OCHA warned Wednesday.

The UN describes the food crisis in drought-hit Somalia as the world's worst ongoing humanitarian disaster.

Uganda, which provides the bulk of the 9,000-strong African Union force protecting the Western-backed Somali government in Mogadishu, welcomed the operation and said Kenya had the right to defend itself.

Ethiopia, the last country to invade Somalia when it toppled an Islamist leadership in 2006, also voiced approval for Kenya's operations, saying the two countries had a "common front in the fight against terrorism."

However, the African Union stopped short of backing the operation.

"I don't say support, I say understand the motivations of the operations, in order to put an end to the capabilities of the Shebab," said Noureddine Mezni, AU spokesman, in response to a AFP question.

Analysts say Kenya has sent at least 2,000 troops into Somalia, but the military would not comment on operational figures.

Ethiopia had tens of thousands of troops in Somalia for two years but failed to root out the Shebab and establish a robust central government.