The base in southwest Somalia was attacked by Shebab fighters early on Friday morning, in the latest incident of an AU Mission in Somalia (AMISOM) base being overrun by the militants.
"We embarked on a search, rescue and recovery operation as a priority," military chief Samson Mwathethe told reporters on Sunday morning in the capital Nairobi. "Our troops are engaging the terrorists."
Kenya has so far declined to say how many of its soldiers are dead, injured or missing but on Sunday a Shebab statement said that more than 100 Kenyan soldiers were killed and others captured.
"Mujahideen fighters... stormed the Kenyan base in the early hours of Friday morning, killing more than 100 Kenyan invaders, seizing their weapons and military vehicles and even capturing Kenyan soldiers alive," said the emailed statement, seen by AFP.
Jihadist websites in Somalia claimed that 12 Kenyan soldiers were captured.
The Shebab frequently exaggerates the number of troops it kills, while AMISOM and the countries that contribute troops to the force rarely give reliable tolls.
A company of around 150 Kenyan soldiers was stationed at the El-Adde base. On Sunday four injured soldiers were returned to Nairobi.
Kenyan officials did not comment on the Shebab claims saying they had to inform next of kin and "verify" information before making it public.
The pre-dawn attack on the Kenyan base in Somalia's Gedo region, bordering Kenya and Ethiopia, was at least the third major assault on isolated AU bases in the last year.
In September, Shebab fighters stormed a Ugandan AMISOM base in Janale district, 80 kilometres (50 miles) southwest of Mogadishu in the Lower Shabelle region.
And in June, Shebab killed dozens of Burundian soldiers when they overran an AMISOM outpost northwest of Mogadishu.
The Shebab, fighting to overthrow Somalia's internationally-backed and AU-protected government, has lost much territory in Somalia but continues to launch attacks there as well as in Kenya, killing at least 67 people at Nairobi's Westgate Mall in 2013 and massacring 148 people at a university in Garissa last April.
