Kenyan troops have crossed into Somalia and have driven out al-Shabab fighters from two bases near the border in a joint operation with Somali soldiers, according to a Somali military commander.
Kenya has said it will hunt the fighters they accuse of being behind several recent kidnappings of foreigners.
Abdi Yusuf, a senior Somali military commander, said on Sunday that fighter jets struck two al-Shabab bases in southern Somalia, but could not confirm if the aircraft belonged to Kenya.
"There have been air strikes in ... al-Shabab bases near Afmadow late yesterday and today. We are heading towards Afmadow now. Al-Shabab have already vacated the town," he said.
Alfred Mutua, the Kenyan government spokesman, said that its troops had entered southern Somalia to fight the al-Shabab, who it says are responsible for attacks on its territory.
In response, al-Shabab called on Somalis to rally and attack the Kenyan troops.
"Kenya violated the territorial rights of Somalia by entering our holy land, but I assure you that they will return disappointed, God willing," Sheikh Hassan Turki, a senior al-Shabab leader, said.
"Mujahideen fighters will force them to test the pain of the bullets."
Turki called on Somalis to stand united against "this blood-thirsty enemy that has crossed into our territories and the apostate Somali militants helping them".
Several witnesses reported heavy troop movement in Kenya's border regions, with lorries full of soldiers heading towards the frontier.
The assault came a day after George Saitoti, Kenya's interior security minister, branded al-Shabab "the enemy" and pledged to attack them "wherever they will be".
Al-Shabab, or the "youth", is an Islamist group that aims to overthrow Somalia's transitional government and impose Islamic rule.
On Saturday, troops from Somalia's UN-backed transitional government wrested control of al-Shabab-held town of Qoqani in the Lower Juba region, which borders Kenya.
In just over the past month, a British woman and a French woman have been abducted from Kenyan beach resorts in two separate incidents.
Two female Spanish aid workers were seized by armed men on Thursday from the country's crowded Dadaab refugee camp, the world's largest with up to 450,000 mainly Somali refugees.
Kenyan authorities have on several occasions expressed fears that rebel groups would infiltrate the Dadaab camps from Somalia, as the border lies barely 100km away.