The US government is offering $27m (£18m) in rewards for information on the whereabouts of six leaders of the Somalia-based al-Shabab group.
The highest reward is $6m for the group’s leader Abu Ubaidah.
He replaced Ahmed Abdi Godane, who was killed in a US drone strike last year.
Among those being hunted is Mahad Karate, also known as Abdirahman Mohamed Warsame, believed to be a key player in the attack on a Kenyan university which killed 148 people.
The group, part of al-Qaeda, is battling the UN-backed government in Somalia and has also carried out a string of attacks in neighbouring Kenya.
On Wednesday, Kenyan security forces destroyed five suspected al-Shabab hideouts in the Bono forest close to the Somali border, according to Reuters news agency.