Iran's Foreign Minister Hossein Amir-Abdollahian. AP
Saudi Arabia cut ties with Iran in January 2016, after its embassy in Tehran and consulate in the second city Mashhad were attacked by protesters following Riyadh's execution of Shia cleric Nimr al-Nimr.
Speaking on a visit to Lebanon, Amir-Abdollahian said he hoped "diplomatic missions or embassies in Tehran and Riyadh will reopen within the framework of dialogue that should continue between the two countries."
He also hailed a potential rapprochement between Iranian ally Syria and Turkey, after their defence ministers met last month.
Iran and Saudi Arabia back opposing sides in various conflicts in the region, including in Syria.
Since April 2021, Iraq has hosted a series of fence-mending meetings between the two sides, but the talks have stalled in recent months, and no meetings have been publicly announced since April 2022.
Iran holds influence over political life in Lebanon and Iraq, where it supports armed groups.
Syria's pro-government Al-Watan newspaper said Amir-Abdollahian was also set to visit Damascus on Saturday, at a time of warming ties between Syria and Turkey.
"We are happy with this dialogue that is taking place between Syria and Turkey," he told a news conference in Beirut on Friday.
"We believe that this dialogue should have positive repercussions benefitting these two countries."
Ankara had long backed rebels opposed to Syrian President Bashar Al-Assad's rule, but after over a decade of war that has seen the government claw back territory with Russian and Iranian support, ties between the two countries have begun to thaw.
In late December the defence ministers of Turkey and Syria held landmark negotiations in Moscow -- the first such meeting since 2011.
Assad had said on Thursday that a Moscow-brokered rapprochement with Turkey should aim for "the end of occupation" by Ankara of parts of Syria.
The defence ministers' meeting would be followed by talks between the three countries' top diplomats, Turkish Foreign Minister Mevlut Cavusoglu said on Thursday.
The mooted reconciliation has alarmed Syrian opposition leaders and supporters who reside mostly in parts of the war-torn country under Ankara's indirect control.