The state of emergency was imposed in mid February after the resignation of former Prime Minister Hailemariam Desalegn which gave rise to a power struggle within the ruling coalition, Ethiopian People's Revolutionary Democratic Front (EPRDF).
"The Eritrean government should take the same stand without any prerequisite and accept our call to bring back the long-lost peace of the two brother nations as it was before", the EPRDF wrote on Facebook.
The news came just hours after Ethiopia lifted a state of emergency in what had been the biggest reform yet under new Prime Minister Abiy Ahmed, who has promised change after more than two years of deadly anti-government protests demanding greater freedoms in Africa's second most populous country.
"While majority stakes will be held by the state, shares in Ethio Telecom, Ethiopian Airlines, Ethiopian Power, and the Maritime Transport and Logistics Corporation will be sold to both domestic and foreign investors", it said in a statement.
Ethiopia became landlocked in 1993 after Eritrea, which comprised the country's entire Red Sea coast, voted to leave.
The agreement was the result of a border commission convened in 2000 after two years of bloody fighting between the two countries over disputed lands along the border, specifically the town of Badme.
The UN Security Council sanctioned Eritrea in 2006 for supporting Al-Shabaab extremists in Somalia, the same year Ethiopia invaded to battle the group.
All legislators in Ethiopia's parliament are members of the ruling party.