Thirty armed Ethiopian troops and large numbers of refugees fled the fighting in Ethiopia's northern Tigray region and crossed into Sudan, state-run Suna news agency reported.
Nobel Peace Prize-winning Ethiopian Prime Minister Abiy Ahmed again promised that his military will bring a speedy end to fighting in the Tigray region and the removal of its leadership, which his government regards as illegal.
On Wednesday, Mr Abiy ordered the launch of a military offensive against the Tigray People's Liberation Front, which he accused of attacking an Ethiopian army base.
Each side blames the other for starting the conflict.
The troops from Ethiopia’s Amhara region neighbouring Tigray fled into Sudan’s Qadarif province on Monday evening, the Suna report said, citing witnesses.
Local authorities began to prepare a refugee camp for the fleeing Ethiopians, it said, while aid groups spoke of a humanitarian crisis affecting millions of people at the heart of the Horn of Africa region.
The Ethiopian troops appealed for protection as fighting raged over the border, said a Sudanese military official.
Mr Abiy described his government’s military campaign in the Tigray region as law enforcement operations that he said will end as soon as "the criminal junta is disarmed, legitimate administration in the region restored, and fugitives apprehended and brought to justice – all of them rapidly coming within reach”.
On Monday, an Ethiopian military official said the air force was “pounding targets with precision”.
Moussa Faki Mahamat, chairman of the African Union, called for an immediate end to hostilities.
In a statement on Monday, he said the AU, based in Ethiopia, was ready to support an inter-Ethiopian effort to pursue peace and stability.
Mr Abiy has shown no sign of opening talks with the Tigray People’s Liberation Front, which once dominated Ethiopia’s ruling coalition. Feeling marginalised by Mr Abiy’s political reforms after he took office in 2018, it broke away last year as the prime minister sought to transform the coalition into a single Prosperity Party. The front defied the federal government by holding a local election in September.
Diplomats and others assert that the conflict in Tigray could destabilise the region and other parts of Ethiopia which has scores of ethnic groups and other regions that have sought more autonomy even as Mr Abiy tries to hold the country together with calls for national unity.
Several hundred people were reported to have been killed on both the Ethiopian government side and the Tigray regional government side, a diplomat in the capital, Addis Ababa, told the Associated Press.
More than 150 citizens of European Union countries alone are thought to be in the Tigray region, where airports and roads are closed, communications are largely severed, and governments are trying to ensure their consular protection, a diplomat said.
Experts said that the longer the conflict lasted, the more difficult it will be for the federal government to bring the Tigray region back to Ethiopia's federation of regional states.
Aid groups said humanitarian needs will grow. A United Nations spokesman told reporters on Monday that discussions were under way on the relocation of all non-essential UN staff and on gaining humanitarian access.
Ethiopia’s state television on Monday showed scenes of federal government troops arriving in the border town of Dansha, to cheers, and of what the report said were Tigrayan militia members after surrendering to federal forces.
