The insurgency's appointed governor of Gedo region, Sheik Da'ud Mohamed Garane, made the threats on behalf of the al-Shabab militia following reports that Kenya's military was stepping up recruitment of ethnic Somalis who are Kenyan citizens.
"Our intelligence sources have already confirmed that Kenya is giving training and military equipment to Somali men in three different areas along its border with Somalia," he told a crowd of some 200 people in southwestern Somalia. "These men are being prepared to attack the peaceful positions we control. But let me tell Kenya that we will do all we can to prevent that to happen."
Somali information minister Dahir Mohamud Gelle has denied the Kenyan military is recruiting near the long and porous border shared by the two countries. Kenyan officials were not immediately available for comment.
Many who live in Kenya's arid northeastern region speak Somali and consider themselves part of that ethnic group.
Islamists have targeted Kenya, a popular tourist destination, before. In 1998 Islamists blew up the American embassies in Kenya and Tanzania, killing 224 people, and in 2002 Islamists bombed an Israeli-owned hotel in Kenya, killing 13 people.
Somalia has been torn apart by civil war over the past 18 years, after warlords overthrew dictator Mohamed Siad Barre in 1991, then turned on each other.
The Islamist insurgency is currently not only battling the U.N.-backed government, but also trying to heal splits in its own alliance that spilled over into a fatal clash last month.