Saudi King Salman bin Abdul Aziz on Sunday met the UN Secretary-General Antonio Guterres.
The Saudi monarch received Guterres at his office in the kingdom's western city of Jeddah, the Saudi official news agency (SPA) reported.
The two sides, according to the SPA, discussed "the developments on the international scene, and various efforts aimed at achieving global peace and stability."
Ethiopian Prime Minister Abiy Ahmed and Eritrean President Isaias Afwerki also arrived in Saudi Arabia on Saturday for a signing ceremony of a historic peace accord between the two countries.
The SPA said that King Salman invited Guterres to attend the signing of the agreement between the two African countries, without mentioning the date of the ceremony.
Eritrea seceded from Ethiopia in 1993, and from 1998 to 2000 the two countries fought a bloody war in which an estimated 70,000 people perished on both sides.
The two countries broke two decades of tension after Ethiopian Prime Minister Abiy Ahmed extended an olive branch to the Eritrean president in his inaugural speech in April.
The men met in July, vowing to revamp relations and Eritrea opened its embassy in Addis Ababa in mid-July.
Ethiopia reopened its embassy last week in the Eritrean capital of Asmara after a 20-year hiatus.