"If not, know that this is just a taste of what we will do... You should expect black days," Shebab spokesman Ali Mohamud Rage said, speaking in Arabic in an audio broadcast released by the extremists.
Kenyan troops invaded southern Somalia to attack Shebab bases two years ago, joining forces with a Somali militia warlord and wresting the key port of Kismayo from the extremists.
Kenyan troops later joined the 17,700-strong African Union force deployed in Somalia.
Shebab fighters stormed the crowded Nairobi mall midday on Saturday, tossing grenades, firing automatic weapons and sending panicked shoppers fleeing.
At least 65 shoppers, staff and soldiers have been killed and close to 200 wounded in the siege, but concerns are high that the toll may rise, with the Shebab boasting about "countless number of dead bodies still scattered inside the mall".