“Politics can divide us but they [Eritreans] are still our brothers and relatives,” Bashir said, according to the AFP news agency.
Bashir made the announcement during a televised address for a rally in the regional capital Kassala. However, he did not provide more details on the decision.
The border was closed in January 2018 in line with a six-month state of emergency in Kassala and North Kordofan. The intention was to stop smuggling, control unlicensed vehicles and tackle human trafficking, the Xinhua news agency reported.
Bashir’s address in Kassala also touched on continuing protests in Sudan that have erupted in Khartoum and other cities since December.
“It’s only the people who decide who will be president,” he added.
Protests started over increases in the price of bread, but have morphed into a more general dissatisfaction with Bashir and his government.
Human rights groups say more than 40 people have been killed in a crackdown by security forces on demonstrations since December. Sudanese officials say 30 people have died in protest-related violence.