The pipeline will run from Eritrea's port city of Assab to Ethiopia's capital Addis Ababa
The UAE is also driven by a fear that rivals such as Iran or Qatar could gain a foothold. Earlier this year ties frayed between Mogadishu and Abu Dhabi and the two countries ended a UAE military training programme in Somalia.
Abu Dhabi has a military base in Assab which it uses in its military campaign in the war in Yemen, located just across the Red Sea.
Saudi Arabia's Foreign Minister Adel al-Jubeir arrived in Addis Ababa on Thursday and met with Abiy, although there were no detailed announcements from the meeting.
Last month, Reuters reported that Ethiopia had asked Saudi Arabia for a year's supply of fuel with payment delayed for 12 months to ease severe foreign currency shortages.
Eritrea's foreign minister and a close adviser to President Isaias Afkwerki arrived in Ethiopia on Friday to discuss progress on implementing the agreement they signed last month.
The rapprochement ended Africa's longest major military stalemate and holds great potential for both economies, which were held back by the "no war, no peace" status quo.
Though the two countries have re-opened embassies in each other's capital and resumed flights, details ranging from border demarcation to war reparations have not been worked out.
