The US commando's death on Friday was the US military's first fatality in Africa since four soldiers were killed in ambush in Niger last October.
One local soldier was also wounded in the attack, the USA military said in a statement, without clarifying whether that fighter was part of the Somali or Kenyan armed forces.
Al-Shabab quickly claimed responsibility for the attack on Telegram via its Shahada News Agency.
The U.S. said a Somali soldier was among the wounded, though witnesses said two Somali soldiers were killed.
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The Shabab said in a post translated by the SITE Intelligence Group, which monitors online extremist message boards, that its fighters had attacked a joint American-Somali base near Kismayo, mounting what it called a "fierce attack".
A Navy SEAL was killed in Somalia in May previous year, marking the first U.S. military combat death there since the infamous "Black Hawk Down" events of 1993, when 18 American servicemen died in the Battle of Mogadishu. The U.S. military said its personnel had provided advice, assistance and aerial surveillance during the mission.
There are about 500 USA troops in Somalia on an advise and assist mission to help the Somali military in its fight against al Shabab, an al Qaeda-affiliated terror group.
"My thoughts and prayers are with the families of our serviceman who was killed and his fellow servicemen who were wounded in Somolia. We also injured four USA soldiers", Abdiasis Abu Musab, al Shabaab's military operations spokesman, told Reuters on late Friday.
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"One of the wounded U.S service members received sufficient medical care in the field".
During a seven-month investigation into the attack, led by officials from the Pentagon's Africa Command, the Special Operations general in charge of American commandos in Africa issued a series of orders that roughly mirrored the actions in Somalia, putting in place stringent guidelines to ensure that those on the ground had the proper support before leaving on a mission.
And at least in Niger, U.S. Africa Command's General Thomas Waldhauser said commanders had been ordered to be "far more prudent" about the missions that were approved.
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