Kenyan fighter jets have attacked two bases belonging to Islamist al Shabaab insurgents in Somalia and killed at least 80 militants, African Union peacekeepers there said.

Al Shabaab rebels denied any of its fighters had been killed.

The African Union Mission in Somalia (AMISOM), whose soldiers launched a new offensive against al Shabaab this year, said Kenyan planes carried out the raids on Anole and Kuday in the southern Lower Jubba region. It did not say when they took place.

"The air strikes in Anole left more than 30 al Shabaab fighters dead, three technical vehicles and one Land Cruiser loaded with ammunition destroyed," AMISOM said. More than 50 rebels were killed in the Kuday raid, it added.

Responding to the AMISOM statement, al Shabaab's spokesman for military operations Sheikh Abdiasis Abu Musab told Reuters the group did not have any bases in the area of the raids, which it said took place on Thursday.

"Only pastoralists were around there and luckily no goat was injured, let alone a civilian," he said.

Kenya first sent its troops into neighbouring Somalia in 2011 after several attacks inside its territory that it blamed on al Shabaab, and later joined the peacekeeping force.

The militants have since carried out a string of assaults to punish Kenya for its intervention. Al Shabaab fighters killed at least 67 people in a raid on a Nairobi shopping mall last year.

AMISOM said al Shabaab had lost control of more than 10 major towns in the new push by African troops, including soldiers from Uganda, Djibouti, Ethiopia, Burundi and Sierra Leone.

"AMISOM continues to up the pressure on al Shabaab with a view to liberating more areas in forthcoming operations," the force said.

Officials and diplomats have said towns cleared of Al Shabaab are in a dire state, with food stocks emptied and largely abandoned by their inhabitants, creating what one envoy described as "ghost towns".

They say al Shabaab still controls tracts of countryside, making it difficult for supplies to be moved to the towns.

Somalia's government is struggling to impose order since the AU peacekeepers, backed by Somali troops, drove al Shabaab out of the capital Mogadishu in 2011.

More than two decades of conflict have left Somalia in ruins, while al Qaeda-linked al Shabaab has continued guerrilla-style attacks and suicide bombings.

Al Shabaab claimed responsibility for last week's attack on the Kenyan coastal town of Mpeketoni that killed about 65 people, although Kenyan President Uhuru Kenyatta dismissed al Shabaab's account and said local politicians were behind it.

In a separate incident, an al Shabaab spokesman said the group had attacked Kenyan troops near the border with Kenya on Monday morning and had burned four trucks, killing those inside.

Kenya's defence forces denied there was any such fight.

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