Saudi Arabia's embassy in Tehran was attacked and damaged in January 2016.
Saudi Arabia confirmed on Sunday it had held its first round of direct talks with Iran's new government last month to reduce tension between the rival powers.
The longtime foes who severed ties in 2016 began talks in April, at a time when Washington and Tehran were discussing reviving a nuclear pact that Riyadh and its allies had opposed.
Three rounds of Saudi-Iranian talks were held in Iraq in the months before Iran's new hardline president, Ebrahim Raisi, took office in August.
Foreign Minister Prince Faisal bin Farhan al-Saud said the latest round had taken place on Sept. 21. He did not give the location of the meeting. The date coincides with a speech by Raisi at the UN General Assembly in New York.
"These discussions are still in the exploratory phase. We hope they will provide a basis to address unresolved issues between the two sides and we will strive and work to realize that," he told a joint news conference.
Saudi Arabia and Iran have backed opposing sides in regional conflicts and political disputes in Syria, Lebanon and Iraq for years, and Saudi Arabia has led an Arab coalition waging war against the Iran-aligned Houthi movement in Yemen since 2015.
Riyadh and Tehran have both said they hope the talks can ease tensions, while playing down expectations of a major diplomatic breakthrough. Iran did not immediately comment on the Sept. 21 round of talks. Riyadh has said it would judge the government of Raisi by the reality on the ground.
Prince Faisal was speaking during a visit to Riyadh by EU foreign policy chief Josep Borrell, who said he had briefed his partners on the prospects for restarting the nuclear talks.
Report by Reuters