Somali and African troops have captured a new town from Shebab Islamists during a major offensive, the army said Thursday, days after US air strikes targeted the extremists' leader.

Troops on Wednesday seized the town of Jalalaqsi, some 150 kilometres (90 miles) north of Mogadishu, and the Al-Qaeda-linked Shebab fled without a fight, the 22,000-strong African Union mission in Somalia (AMISOM) said in a statement.

"Al-Shebab militants did not mount any serious battle and fled the town as Somali army and AMISOM forces entered," AMISOM said.

"The momentum will continue until the terrorism threat is dealt with," said Somali army chief Dahir Adan Elmi.

The fate of Shebab chief Ahmed Abdi Godane remains unclear, three days after a US missile strike targeted his convoy.

Security sources have said his death is a "very strong probability", but Shebab officials have so far refused to confirm or deny the reports.

If confirmed, the death of Godane would be a major blow to the Islamists.

The US State Department lists him as one of the world's eight top terrorist fugitives, and have offered a $7-million (5.35-million-euro) reward for information.

The military advance, called "Operation Indian Ocean", is aimed at seizing key ports from the Islamist rebels and cutting off one of their key sources of revenue -- multi-million dollar exports of charcoal.

The capture of Jalalaqsi in the Hiran region was on a separate front from the main advance, which is in coastal regions southwest of Mogadishu, the capital.

The Shebab are fighting to topple Somalia's internationally backed government, and regularly launch attacks against state targets.

They also strike in neighbouring countries that contribute troops to the African Union force -- including last year's siege of the Westgate shopping mall in the Kenyan capital Nairobi that left at least 67 dead.

As the offensive gathers pace, Somalia's fragile government has offered an amnesty to insurgents, saying they are willing to give "misled" Shebab members one last chance to surrender.

In previous offensives by AU troops, Shebab fighters have fled before main offensive, only to later returned to stage guerrilla-style attacks.

Shebab fighters continue to launch attacks even in the heart of Mogadishu, including recent brazen commando raids on the presidential palace and parliament.

UN and aid workers warn large areas of Somalia are struggling with dire hunger and drought, three years after famine killed more than a quarter of a million people.