Iran says Saudi Arabia has invited Iranian President Ebrahim Raisi for an official visit – just over a week since the countries agreed to restore diplomatic relations.
The invitation is said to have come in a letter from King Salman, but has not yet been confirmed by the Saudis.
The Middle East’s recent history has been dominated by hostility between the two nations.
China brokered the thaw, which could reshape the region’s geopolitics.
A senior Iranian official, Mohammad Jamshidi, tweeted about the invitation to visit the Saudi capital, Riyadh, saying Mr Raisi had welcomed it and “stressed Iran’s readiness to expand co-operation”.
Separately, Iran’s Foreign Minister Hossein Amir-Abdollahian told reporters that the two countries had agreed to hold a meeting at foreign minister level, and that three possible locations had been proposed.
He did not name the locations, nor say when the meeting might take place.
The BBC’s Middle East Editor, Sebastian Usher, says the recent improvement in bilateral relations, which came unexpectedly following days of talks brokered by China, appears to be building serious momentum.
Both have announced they will reopen embassies within two months and re-establish trade and security relations.
This development was cautiously welcomed by many, including the US and the United Nations, after previous attempts at reconciliation were unsuccessful.
Saudi Arabia cut ties in January 2016 after demonstrators stormed its embassy in Tehran.
That was after Riyadh had executed the prominent Shia Muslim cleric Sheikh Nimr al-Nimr, who was convicted of terror-related offences.
Since then, tensions between the Sunni- and Shia-led neighbours have often been high, with each regarding the other as a threatening power seeking regional dominance.
They have been on opposing sides of several regional conflicts, including the civil wars in Syria and Yemen.
Mr Amir-Abdollahian also said that Iran hoped steps would be made to improve ties with Bahrain, a close Saudi ally that followed Riyadh in severing diplomatic ties with Tehran in 2016.
“We hope that some obstacles between Iran and Bahrain will be removed and we will take basic steps to reopen the embassies,” he said.
Bahrain has not responded to the comments, but earlier welcomed the Iran-Saudi agreement to restore diplomatic ties.
Iran has also expressed a willingness to resume or improve relations with other regional Arab rivals, including Jordan and the United Arab Emirates.