There was no independent confirmation of the strikes in response to Saturday's attack by the Al-Qaeda-linked group near Mandera, a northeastern town near the Kenya-Somali border.
But the Shebab swiftly rubbished Kenya's claim, calling it 'totally baseless and unfounded'.
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"Following the Mandera bus attack, our security forces swiftly initiated a response. They identified, followed and struck the perpetrators of these heinous crimes," Kenya's Vice-President William Ruto said in a statement.
He said Kenyan troops carried out two successful operations, causing 'more than 100 fatalities' as well as destroying four trucks carrying weaponry and smashing the camp where the attack was planned.
The Shebab's military spokesman Abdulaziz Abu Musab however said that its militants 'did not face any attack whatsoever after the successful operation they carried out'.
"We have seen the absurd claim by the Kenyan authorities that they killed our mujahideen who carried out the Mandera attack, a totally baseless and unfounded claim," he said.
"Claims like these are only spewed by the Kenyan authorities to cover up their failure to secure the safety of their people, and in an attempt to douse the raging anger of the Kenyan public, after the severe blow the mujahideen delivered to them," he added.
Shebab fighters executed the passengers after seizing a bus carrying some 60 people in what they said was revenge for police raids on mosques in the troubled port of Mombasa.
The bus, headed for the capital Nairobi, was ambushed shortly after departing from Mandera in the deadliest attack in months.
Passengers were ordered off the vehicle and the travellers separated by the gunmen into Muslims and non-Muslims.
The groups made up of dozens of militants then forced the non-Muslims to reboard the bus and tried to drive off with them. But the vehicle got stuck, so they executed their prisoners before escaping back into Somalia.
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