Abiy arrived at Khartoum international airport and headed for a series of meetings with the ruling generals, an AFP correspondent reported from the airport.
The Ethiopian premier was scheduled to meet protest leaders later.
"We have received an invitation from the Ethiopian embassy to meet the Ethiopian prime minister at 11:00 a.m. [0900 GMT] and we will go," prominent protest leader Omar al-Digeir told AFP.
On Monday, Sudanese security forces launched a deadly crackdown on a weeks-long sit-in outside army headquarters in which more than 100 people were killed, according to the protest movement.
Officials have put the death toll at 61 nationwide.--AFP