Ethiopian forces have captured the central Somali town of Beledweyne from al-Shabab Islamist militants.
Al-Shabab said its forces were surrounding the town after making what it called a planned withdrawal.
Eyewitnesses said armoured vehicles and heavy artillery were used in the attack, which Ethiopia said was made at the request of the Somali government.
Somalia's prime minister meanwhile announced an operation "to liberate the tyranny of... al-Shabab from Somalia".
"Early this morning, the Somali National Army recaptured some al-Shabab-occupied territories engaging the enemies in Hiiraan and other regions of the country," said Abdiweli Mohamed Ali, head of Somalia's Transitional Federal Government (TFG)
"We are officially requesting for momentous support from neighbouring countries such as Ethiopia and the international community at large to assist the Somali people and its government with this historic operation."
Al-Shabab fighters withdrew from Beledweyne after a fierce hours-long battle in which local residents had joined "the Mujahideen" to fight against more than 3,000 Ethiopian troops, according to messages posting on a twitter account reportedly run by al-Shabab's press office.
"Sheikh Abu Mus'ab, HSM Military Spokesman, has declared a planned withdrawal from the city and Mujahideen are now surrounding the city," read a tweet posted around 11:30 GMT on Saturday.
Twenty people were killed in the fighting, a BBC Somali reporter said, mostly Ethiopian troops and al-Shabab fighters.
Beledweyne is a strategic town near the Ethiopian border on the road to Somalia's capital, Mogadishu.
It was through the town that Ethiopia entered the country during 2006 and from it that its troops were driven in 2008, finally withdrawing back into Ethiopia, says BBC Africa analyst Martin Plaut.
An Ethiopian government spokesman, Bereket Simon, told the BBC's Newshour programme: "The TFG has called on neighbouring countries including Ethiopia to assist this operation militarily so that's why we have entered."
Last month, Ethiopia denied that its troops had returned to Somalia - about two years after they withdrew after suffering heavy casualties.
The AU has about 9,000 troops in Mogadishu under a UN Security Council mandate to battle the al-Qaeda-linked group.
Foreign military intervention in Somalia is intended to prevent al-Shabab from overthrowing the weak interim government led by Somalia's President Sheikh Sharif Ahmed - a moderate Islamist.
Al-Shabab announced a "tactical withdrawal" from Mogadishu in August after fierce fighting with AU forces.
AU commanders in Somalia say they need about 20,000 troops to hold on to territory captured from al-Shabab.
Somalia has not had a functioning central government for more than 20 years and has been wracked by fighting between various militias.