In a statement that underscored the group's ambition to expand its operations, Shebab leader Ahmed Diriye, also known as Ahmed Umar Abu Ubaidah, took aim at Kenya, Ethiopia, Djibouti and Uganda.
"The sword of the Mujahedeen is drawn and attacks against the enemy are ongoing countrywide and we are calling them to increase their attacks on the infidels," he said in a statement posted on an Islamist website.
"We say to our beloved brothers living in territories under Kenyan colonisation that your brothers will never stop coming to your assistance," he said.
Diriye praised the April massacre at Garissa university in northeastern Kenya, in which four Shebab gunmen killed 148 people, most of them students. The attackers were mostly Muslims from Kenya.
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"We congratulate you and the rest of the Muslims in the world on the heroic Garissa university operation," the Shebab leader said, saying the massacre was retaliation for "organised extrajudicial killings against clerics and kidnappings of Islamic youth" along Kenya's Muslim-majority coastline.
"We will not spare any effort to assist you, and the doors of our training camps are open to receive you and our houses are open to welcome you."
The Shebab, meaning "youth" in Arabic, emerged out of a bitter insurgency against Ethiopia, whose troops entered Somalia in a 2006 US-backed invasion to topple the Islamic Courts Union that was then controlling the capital Mogadishu.
Currently affiliated to the Al-Qaeda franchise, there has been mounting speculation that the group could shift its allegiance to the Islamic State group.