Both steps represent major policy changes by Abiy, the first prime minister in modern Ethiopia from the country's largest ethnicity the Oromo who took office in April after years of anti-government protests and political turmoil.
It says it will accept the outcome of a 2002 border commission ruling, which awarded disputed territories, including the town of Badme, to Eritrea.
Ethiopia on Tuesday cut short a state of emergency imposed after the resignation of the former prime minister, a move hailed as a positive sign the new government is breaking with the past. Eritrea had accepted EEBC's decision and refused to submit to any further negotiation without the prior acceptance by Ethiopia of the commission's decision.
In a stunning departure from its own economic policy, the EPRDF has also made a decision to transfer shares in mega state owned including the national carrier Ethiopian Airlines, state monopolies Ethio-telecom & Ethiopian Shipping and Logistics Service Enterprise, and hydroelectric projects both to Ethiopians and foreign investors.
The move would "enable Ethiopia-born citizens living overseas who've long wished to work on the development of their country, and. foreigners who have the knowledge and foreign currency, to play a positive role in our growth", said the statement issued after a meeting of top EPRDF officials.
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A one-time province of Ethiopia enjoying its entire Red Sea coastline, Eritrea voted for independence in a 1993 referendum but was soon at war with its southern neighbour over the demarcation of the two countries' borders.
The UN Security Council sanctioned Eritrea in 2006 for supporting Al-Shabaab extremists in Somalia, the same year Ethiopia invaded to battle the group.
Parliament approved a bill on Tuesday to end the emergency rule two months earlier than planned, state-affiliated Fana Broadcasting reported.
The Oromos are Ethiopia's largest ethnic group and make up around a third of the nation's 100 million population.
That unrest left hundreds dead and resulted in tens of thousands of arrests and the imposition of an earlier 10-month state of emergency in October 2016.