The UN wants humanitarian corridors set up after two weeks of conflict between Ethiopia’s military and forces backing the leadership in the Tigray region.
Hundreds of people are reported to have been killed in the clashes.
On Friday Ethiopia’s government said it had captured the city of Aksum and the town of Adwa.
The government said that forces battling its military in both areas had “surrendered”.
However, the claims have not been independently verified and information is difficult to confirm because phone and internet connections have been down since the beginning of the conflict.
Aksum is one of the largest cities in the Tigray region and the mountainous town of Adwa is also considered strategically important.
Earlier this week, central government forces seized two other towns in Tigray – Shire and Raya – and Prime Minister Abiy Ahmed said his army was advancing on the Tigrayan capital, Mekelle.
Ethiopia has so far rejected calls for talks over the crisis, seeing its operation as internal “law enforcement”.
The conflict is rooted in long-standing tension between powerful regional party the Tigray People’s Liberation Front (TPLF) and Ethiopia’s central government.
When Mr Abiy postponed a national election due to coronavirus in June, tension escalated between the two sides. The TPLF sees the central government as illegitimate, arguing that Mr Abiy no longer has a mandate.
Aid agencies have no access to the conflict zone, but they fear that thousands of civilians may have been killed since fighting erupted at the beginning of November.
At least 33,000 refugees have already crossed Ethiopia’s border into Sudan and the UN refugee agency has said it is preparing for up to 200,000 people to arrive over the next six months if the fighting continues.
On Friday, the TPLF was accused of firing rockets into the city of Bahir Dar in the neighbouring Amhara region. The Amhara government said there were no casualties and no damage caused.
But the reported incident in Amhara, which has a long-running border dispute with Tigray, has raised concerns that the conflict could extend into a wider war after regional forces were sent to support federal
Meanwhile, the UN has raised concerns about the influx of refugees into Sudan, which it says could destabilise a nation already supporting about a million people displaced from other African countries.
The refugees arriving in Sudan, the majority of whom are believed to be children, are hungry and frightened, aid agencies say, and an immediate ceasefire would allow them to help thousands of civilians still trapped inside Ethiopia.