Kenya has every right to pursue al Shabaab rebels in Somalia, but Somali government troops must be in charge of operations against the Islamist rebels, Somalia's prime minister said.

Kenya deployed troops inside the anarchic Horn of Africa nation 12-days ago in an offensive against al Shabaab fighters it blames for a series of kidnappings on its soil and frequent cross-border incursions.

Somalia's president cast doubt on his government's support for the incursion Monday. Wednesday, Mogadishu reiterated there was no deal with Kenya to send in its troops, but said the prime minister would now liaise with Nairobi.

We support Kenya's operation inside Somalia because they support, train and provide other military support to our troops to defeat al Shabaab and we are very grateful to Kenya, Prime Minister Abdiweli Mohamed Ali said in an interview.

But we have to understand one thing: Somalia has the lead, our military has the lead in all operations taking place inside Somalia, he said late Wednesday.

The Somali government has so far stopped short of asking Kenyan troops to leave and the prime minister's comments show the authorities appear to accept the incursion, which has the backing of Western allies supporting the Mogadishu government.

My government supports any self defence action Kenya takes against al Shabaab. Al Shabaab has inflicted a negative economic impact on Kenya, the prime minister said.

Kenya has suffered at the hands of al Shabaab who are Somali terrorists crossing from the Somali border to the Kenyan border. So, therefore, Kenya has the right to pursue them inside Somali and defeat them, he said.

East Africa's biggest economy has long watched its anarchic neighbour warily and its troops have made forays across the porous border in the past, but this month's assault marks the first concerted push to drive the rebels away from the frontier.

The recent kidnappings of Western tourists and aid workers from Kenya soil risk denting the country's lucrative tourist industry and hampering humanitarian support for more than 400,000 Somalis at a refugee camp in northern Kenya.

Al Shabaab has denied it is behind the kidnappings, saying they are being used as a pretext by Kenya to send its troops across the border.

Kenyan troops are advancing on several fronts towards al Shabaab strongholds alongside Somali government soldiers and allied militias in the region.

The Kenyan troops have taken several towns but have not yet had a major showdown with al Shabaab fighters, who are regrouping and bolstering defences at strategic points in the south of the Horn of Africa nation.

Kenya continued to deploy more troops to Somalia on Wednesday. Trucks laden with weapons, military and police officers from the capital and camps in central and northern Kenya were seen heading towards Somalia.

(Additional reporting by Noor Ali in Isiolo, Kenya; Editing by David Clarke)