In an interview with Al Jazeera, Hossein Amirabdollahian said King Salman had invited President Ebrahim Raisi of Iran for a trip to the kingdom, and that Tehran will likewise send an invitation for the monarch to make a visit to Iran.
Earlier this month, Tehran and Riyadh announced a surprise reconciliation agreement, brokered by China, following a seven-year-long rupture in their relations.
Amirabdollahian is also expected to meet his Saudi counterpart in the coming weeks.
The two top diplomats have already spoken on the phone.
Elsewhere in the interview, the Iranian foreign minister made comments on the stalled negotiations on the revival of the 2015 nuclear agreement.
He spoke of a bill on the agenda of the Iranian Parliament, which would set a time limit for negotiations on restoring the troubled deal, which the US unilaterally abandoned in 2018.
The chief diplomat warned that the door will not remain open to the talks forever.
The negotiations have been at an impasse for months due to a host of reasons, including a diplomatic dispute with the UN nuclear watchdog and an apparent lack of seriousness in Washington to effectively remove anti-Iran sanctions and return to the nuclear deal.
