Al Shabaab's report on the Sunday attack at Manda Bay Airfield in Lamu County was exaggerated, the US military has said. Manda Bay is an area where US forces provide training and counter-terrorism support to East African partners.
Following the ambush at dawn, the terror group issued a statement, saying there were "severe casualties on both Kenyan and American troops stationed there".
It added: "The Mujahideen fighters covertly entered enemy lines, successfully stormed the heavily fortified military base and have now taken effective control of a part of the base."
But the US Africa Command, Africom, dismissed the group's statement, saying the message was distorted to create the wrong impression.
"Al-Shabaab resorts to lies, coercion, and the exertion of force to bolster their reputation to create false headlines," said Maj-Gen. William Gayler, US Africa Command's Director of Operations.
Al-Shabaab also claimed it seized part of the military base and that fighting was ongoing.
Africom, however, noted that the airfield had been cleared and was being secured.
"The security situation at Manda Bay is fluid. Al-Shabaab is a terrorist group that has repeatedly communicated an intent to attack US interests. It is important to counter al-Shabaab where they stand to prevent the spread of this cancer."
The command said more information will be released after personnel are accounted for.
In its statement, the Kenya Defence Forces (KDF) said the attackers were successfully repulsed by multi-agency forces.
"Arising from the unsuccessful breach [was a fire that affected] some of the fuel tanks at the airstrip. The fire has been put under control and standard security procedures are ongoing," the statement posted on its official social media pages also said.
Military spokesman Colonel Paul Njuguna said five bodies of al-Shabaab fighters were found and that they were searching for others.
Colonel Njuguna said they found a PKM gun, four RPG launchers, four AK-47 rifles, a hand grenade and assorted ammunition.
Regarding al-Shabaab's account, he said, "Terrorists are known for propagating false and misleading information in an attempt to grab headlines and feed their egos. Their contorted plans have not and will never succeed."
He added: "Multi-agency forces charged with defending and protecting the sovereignty and territorial integrity of our republic will continue to pursue and destroy these forces of evil until they are smoked from their caves and permanently destroyed."
Earlier, Lamu County Commissioner Irungu Macharia said five suspected terrorists had been arrested in connection with Sunday's attack.
Lamu residents had been assured of security following an attack by al-Shabaab on two buses in Nyongoro.
Following the incident on Thursday, Kenyan soldiers reported that they had killed four al-Shabaab militants and captured one.