The Saudi and Iranian foreign ministers spoke by phone to mark the beginning of Ramadan, vowing to meet "soon" to implement a landmark bilateral reconciliation deal, Riyadh said on Thursday.

The Saudi minister, Prince Faisal bin Farhan, called Hossein Amir-Abdollahian and the pair "exchanged congratulations on the occasion of the holy month of Ramadan", which begins Thursday in both countries, the Saudi foreign ministry said in a statement posted on Twitter.

"The two ministers agreed to hold a bilateral meeting soon in order to pave the way for the reopening of embassies and consulates between the two countries," the statement said.

Saudi officials have said the ministers' expected meeting is the next step in a surprise Chinese-brokered rapprochement announced on March 10 intended to fully restore diplomatic ties seven years after they were severed.

Riyadh cut relations after Iranian protesters attacked Saudi diplomatic missions in 2016 following the Saudi execution of Shiite cleric Nimr al-Nimr -- just one in a series of flashpoints between the two longstanding regional rivals.

The deal is expected to see Shiite-majority Iran and mainly Sunni Muslim Saudi Arabia reopen their embassies and missions within two months and implement security and economic cooperation deals signed more than 20 years ago.

On Sunday, an Iranian official said President Ebrahim Raisi had favourably received an invitation to visit Saudi Arabia from King Salman, though Riyadh has yet to confirm.

Amir-Abdollahian told reporters the same day that the two countries had agreed to hold a meeting between their top diplomats and that three locations had been suggested, without specifying which.

The detente between Saudi Arabia, the world's biggest oil exporter, and Iran, strongly at odds with Western governments over its nuclear activities, has the potential to reshape relations across a region characterised by turbulence for decades.