In a tweet posted in Arabic language, Amirabdollahian said the Saudi foreign minister said during the session that the kingdom was ready for a continuation of negotiations with Iran.
The chief Iranian diplomat did not elaborate on the content of the discussions.
He said he also sat down for talks with foreign ministers of other neighboring Arab countries, including Oman, Qatar, Iraq and Kuwait.
Iran and Saudi Arabia have held several rounds of negotiations in the Iraqi capital, Baghdad, in an effort to hammer out their differences and mend their troubled ties.
As the talks were progressing, a new diplomatic standoff broke out between the two sides as Tehran accused Riyadh of having a hand in a set of anti-government protests and deadly riots in Iran by supporting terror groups and launching a media war against the Islamic Republic.
Saudi Arabia cut off diplomatic ties with Iran in January 2016 after Iranian protesters, enraged by the Saudi execution of prominent Shia cleric Sheikh Nimr Baqir al-Nimr, stormed its embassy in Tehran.
Iran has been criticizing the kingdom for pursuing what it calls a confrontational foreign policy toward the Islamic Republic.
Saudi Arabia accuses Iran of supporting the Houthis, fighting the Riyadh-led coalition.
Meanwhile, Iran says Saudi war on Yemen and its support for the Takfiri groups are among major issues blocking the normalization of their ties.
