Tensions in the border region have flared since the outbreak of conflict in Ethiopia's northern Tigray region in early November and the arrival of more than 50,000 mainly Tigrayan refugees in eastern Sudan.
Disputes have been concentrated on agricultural land in al-Fashqa, which falls within Sudan's international boundaries but has long been settled by Ethiopian farmers.
There have been armed clashes between Sudanese and Ethiopian forces in recent weeks, with both sides accusing the other of instigating the violence. The two countries held talks this week in Khartoum over the issue.
"We believe in dialogue to solve any problem," Sudan's information minister, Faisal Salih, told Reuters. "But our army will do its duty to take back all our land. Currently our army has taken back between 60% and 70% of Sudanese land."
Sudanese forces had acted defensively, and clashes had subsided in the past two days, Salih said.
"Sudanese intelligence reports confirmed that the organisation, training and arming of the forces that attacked were not militias but regular forces," he added.
Ahead of the talks this week, Ethiopia's foreign minister, Ato Demeke Mekonnen said the Sudanese military had carried out attacks beginning on Nov. 9.
"Agricultural products of Ethiopian farmers are looted, their camps are vandalized, and they are also hampered from harvesting their own farms. A number of civilians have been murdered and wounded," he said.
Ethiopian Prime Minister Abiy Ahmed blamed "parties with hidden motives to create hostility and suspicion between peoples" for the violence, in a statement issued on Thursday.
Sudanese officials say the border was demarcated in the first years of the 20th century, and that negotiations are limited to talks over placing additional markers on the land at 2km rather than 10km intervals.