Abiy expressed readiness to hold talks with the Somali government to end the misunderstanding.
The situation remains tense as the local community grapples with the aftermath.
Ethiopian forces will not be included in the African Union-led contingent set to operate in Somalia once the African Union Transition Mission in Somalia (ATMIS) concludes.
The diplomatic rift deepens against the backdrop of a recent meeting between Ethiopia's State Minister of Foreign Affairs, Mesganu Arga, and Mohammed Farah Mohammed, Puntland's regional Finance Minister on Wednesday.
He claims the Somalia Government moved from being "extremely grateful" to "completely disregarding" Ethiopia's support towards fighting the Al-Shabaab militant group.
Ali Omar Balad, Somalia's acting Minister of Foreign Affairs and International Cooperation, affirms their stance against annexation but says they are willing to cooperate with Ethiopia on commercial access.
Al-Shabaab’s persistence has convinced Turkey that it needs to provide more active military support for Somalia’s development. Ankara also wants to protect its economic and political investments in Somalia.
Their statement did not directly mention Somalia, which accuses Ethiopia of attempting to annex its territory through a sea access pact with the beakaway region of Somaliland.
Hassan has said he would only agree to discuss the matter with Ethiopian Prime Minister Abiy Ahmed when the government in Addis Ababa renounces its intention "to take part of our country".
The Ethiopian Mission highlighted what they perceive as outright false information and unjustifiable accusations made by Somalia's officials.
US Assistant Secretary of State for African Affairs Molly Phee and Horn of Africa Special Envoy Mike Hammer emphasised the importance of Somaliland's status being determined by the Somali people, not external actors.
The President is expected to make a major announcement on a special defence agreement with Turkey aimed at reinforcing Somalia's maritime security.
Somalia's Foreign Ministry condemned Ethiopia's "provocative attempt" to block the Somali President's delegation from attending the 2024 AU summit.
Prime Minister Abiy Ahmed says Ethiopia is a second home to Somalis and that the two nations have a bond fortified by blood ties.
At the Rome summit, President Hassan reiterated that his country does not take the matter lightly and that there will be “no room” for mediation with Ethiopia.
In his comments on the situation thus far, Redwan explained that "the signed MoU with Somaliland is a deal for cooperation and partnership that grants Ethiopia access to sea on business terms".
El-Sisi noted that Somalia's rights are enshrined in The Charter of the Arab League - the common defence against any threat to it.
Tensions in the Horn of Africa have escalated since landlocked Ethiopia struck a deal with Somaliland on January 1 that gives it much sought-after access to the sea.
The G77+China summit follows two others that also took place in Uganda - the 42nd ExtraOrdinary Session of the IGAD Assembly of Heads of State and Government and the Non-Aligned Movement (NAM) Summit.
