Ethiopian Prime Minister Meles Zenawi has admitted for the first time that his troops are fighting in Somalia.
The government is getting military help from Ethiopia
Mr Meles said his country was forced to go to war to defend its sovereignty against what he called terrorists and anti-Ethiopian elements.
His troops have been attacking fighters from the Union of Islamic Courts (UIC) in four areas of southern Somalia.
The BBC's Amber Henshaw in Addis Ababa says there has been a significant escalation in the conflict.
The UIC, which has seized control of much of southern and central Somalia, says Ethiopian troops have been fighting alongside government forces for months.
Fighting between the transitional government and forces loyal to the UIC now stretches over 400km (250 miles), our correspondent says.
"As of today our defence forces have launched a counter-offensive, which is completely legal and proportional, on these anti-peace forces [the UIC]," Mr Zenawi said.
"We are not trying to set up a government for Somalia, nor do we have an intention to meddle in Somalian internal affairs. We have only been forced by the circumstances.
"We want to end this war urgently and we hope that Ethiopian people stand by the defence forces."
Speaking in Addis Ababa, the Somali ambassador, Abdikarin Farah, who represents the transitional government, said it was still ready to negotiate with the UIC.
"We are not the people who are pushing the war; we are not the people who are advancing. We are only defending ourselves - that's it. But still the negotiation, it's open and we are ready to have some kind of ceasefire."
Ethiopia says its forces have killed hundreds of Islamists, but Ibrahim Hassan Addow, foreign secretary for the UIC, told the BBC the Ethiopians were lying and that his forces were holding their own.
Air strikes and shelling have been reported in border areas. Eyewitnesses said Ethiopian fighters were bombarding the UIC-held town of Beledweyne near the border, on the fifth day of renewed fighting.
"The enemy of Allah has started bombing our civilians," Sheikh Hassan Derrow told AFP news agency.
A resident told AFP: "We see planes striking us and heavy fighting on the ground intensifying."
Ethiopia, however, denies that its jets have dropped bombs.
The Islamist group - which controls most of the south, including the capital, Mogadishu - on Saturday appealed for foreign fighters to join its troops in a "holy war" against Ethiopia.
The UN estimates that at least 8,000 Ethiopian troops may be in the country, while rival Eritrea is said to have deployed some 2,000 troops in support of the Islamic group.
However, Eritrean President Isaias Afewerki denied his country had troops deployed in Somalia.
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