The two traditional rivals agreed to normalize relations in a March 10 deal brokered by China. Iran's international outreach to its regional rival comes amid major domestic unrest.
Iranian President Ebrahim Raisi on Sunday "welcomed" an invitation from Saudia Arabia's King Salman to visit the country, an Iranian official said.
"In a letter to President Raisi... the King of Saudi Arabia welcomed the deal between the two brotherly countries, [and] invited him to Riyadh," Mohammad Jamshidi, the Iranian president's deputy chief of staff for political affairs, wrote on Twitter.
Also on Sunday, Iranian Foreign Minister Hossein Amirabdollahian said that Tehran had suggested three locations for a meeting with his Saudi counterpart.
"An agreement was reached two months ago for Iranian and Bahraini technical delegations to visit the embassies of the two countries," he said. "We hope that some obstacles between Iran and Bahrain will be removed and we will take basic steps to reopen the embassies,"
Iran and Saudi Arabia agreed to re-establish relations and re-open embassies on March 10 in a deal brokered by China.
The two countries have for many years vied for supremacy in the Middle East, supporting rival factions in the wars in Yemen and Syria. Saudi Arabia formally cut ties with Iran in 2016 after its embassy in Tehran was stormed over Riyadh's execution of a Shiite Muslim cleric.