US forces have carried out air strikes against senior members of Somalia's Al-Qaeda-linked Shebab rebels, with casualties reported but uncertainty hanging over the fate of the group's leader, officials said Tuesday.

The Pentagon confirmed an "operation" was carried out on Monday against the hardline militia, and that it was "assessing the results".

"The Americans carried out a major air strike targeting a gathering by senior Al-Shebab officials, including their leader Abu-Zubayr," said Abdukadir Mohamed Nur, governor for southern Somalia's Lower Shabelle region.

Abu-Zubayr is the often-used name for Shebab supreme commander Ahmed Abdi Godane, listed by the US State Department as one of the world's eight top terror fugitives.

If confirmed, Godane's death would be a major blow for the Shebab -- although Somali officials said late Tuesday they were still trying to establish who was killed.

"The Shebab suffered big casualties during the attack. We can't give further details until we get additional information on the exact number of casualties, but what I know is that the target was the leadership," government spokesman Ridwan Haji Abdiweli told reporters.

Washington has carried out a series of drone missile strikes in the past, including attacks reportedly targeting Godane.

"We are assessing the results of the operation," Pentagon Press Secretary Rear Admiral John Kirby said in a statement.

- $7 million reward -

The Shebab refused to be drawn on speculation that Godane had been killed.

"Let the Americans say that they have killed Shebab's leader," a senior Shebab official told AFP. "So far the Americans just gave us rumours."

The air strike comes days after African Union (AU) troops and government forces launched "Operation Indian Ocean", a major offensive 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.

"They were meeting to discuss the current offensive in the region," Nur said. "There were casualties inflicted on the militants."

Nur said the strike hit a Shebab hideout used as a training camp for suicide bombers a in remote village of the Lower Shabelle region, south of the capital Mogadishu and seat of Somalia's internationally-backed but fragile government.

On Saturday the AU mission in Somalia, AMISOM, said it had captured the town of Bulomarer, some 160 kilometres (100 miles) southwest of Mogadishu.

The town was the scene of an attempted raid by French commandos in January 2013 to free an intelligence agent being held hostage. The bid failed and resulted in the death of two members of the French special forces as well as the hostage.

AMISOM and Somali government troops were also seen on roads towards Barawe, the last major port held by the hardline Islamists,.

As the offensive gathers pace, authorities in Mogadishu said they were willing to give "misled" Shebab members one last chance to surrender.

"They can surrender within 45 days, but anyone who stands against that offer will be recognised as a criminal and brought to justice," Somalia's minister for national security, Khalif Ahmed Ereg, told reporters.

Godane, 37, who reportedly trained in Afghanistan with the Taliban, took over the leadership of the Shebab in 2008 after then chief Adan Hashi Ayro was killed by a US missile strike.

Al-Qaeda chief Ayman al-Zawahiri has recognised Godane as the head of the "mujahedeen" in East Africa, although letters released after Osama bin Laden's death show the late Saudi Islamist leader had lower regard for the Somali's abilities.

He is included in a third category of men on whom information warrants a $7-million (5.35-million-euro) reward from the US, alongside Nigeria's Boko Haram leader, but under the Taliban's Mullah Omar, for whom a tip is worth up to $10 million, and Zawahiri, who fetches $25 million.

- 'A major blow' -

"If confirmed, the death of Ahmed Godane could deal a major blow to Al-Shebab, and could be the beginning of the end," said Abdi Aynte, who heads the Mogadishu-based Heritage Institute think tank.

"The irony is that Godane killed (his) would-be obvious successor, Ibrahim al-Afghani, in a major internal rift last year," Aynte added, saying Godane had structured the Shebab "to bury the organisation with him".

Clint Watts, fellow of the Homeland Security Policy Institute at George Washington University, said if Godane had been killed it would have a "significant impact" and that the group would be likely to splinter.

The Shebab are fighting to topple the government, and regularly launch attacks against state targets, as well as in neighbouring countries that contribute to the AU force.

The US strike comes as the United Nations and aid workers warned that large areas of Somalia are struggling with dire hunger and drought, three years after famine killed more than a quarter of a million people.