Kenyan President Uhuru Kenyatta on Tuesday vowed to defeat al-Shabaab, while the Kenyan air force bombed parts of southern Somalia in retaliation for an attack by the Islamist group which killed Kenyan peacekeepers last week.
Al-Shabaab has said that the attack on an African Union military base in the village of El-Ado killed 100 Kenyan peacekeepers, but Nairobi is yet to give a death toll.
"These enemies of humanity struck at brave patriots, who are in Somalia to protect our families, our nation and the world," Kenyatta said in a televised address to the nation.
"To those misguided elements who think their cowardly actions have shaken us, let me tell them today that their actions have only made us stronger and emboldened us in our determination to defeat them," he added.
Somali officials and witnesses meanwhile the Kenyan airstrikes had killed more than 19 civilians.
Abdiqani Ibrahim, a resident of the village of Arabow, said he saw the bodies of more than 13 civilians, most of whom were pastoralists.
A Somali security official who did not want to be named accused Kenya of indiscriminately bombing villages.
Al-Shabaab militants on Friday attacked the AU base run by Kenyan peacekeepers in El-Ado. Kenyan airstrikes drove the Islamists from the village on Monday.
The Kenyan army meanwhile flew home four bodies of soldiers killed in Friday's attack, in coffins draped in Kenyan flags. Four had already arrived on Monday. They were expected to get a state funeral.
Kenyan troops are part of a 20,000-member AU force helping Somalia battle al-Shabaab.