Saudi Arabia's king and crown prince congratulated Masoud Pezeshkian on his election as Iran's president, state news agency SPA reported on Saturday.
"I affirm my keenness on developing and deepening the relations between our countries and people and serve our mutual interests," SPA quoted Saudi Crown Prince Mohammed bin Salman as saying.
In March 2023, Iran and Saudi Arabia signed a landmark China-brokered deal to re-establish relations after years of regional rivalry.
Friday's run-off vote was between Pezeshkian, the sole moderate in the original field of four candidates, and hardline former nuclear negotiator Saeed Jalili.
Pezeshkian, a 69-year-old cardiac surgeon, has pledged to promote a pragmatic foreign policy, ease tensions over now-stalled negotiations with major powers to revive a 2015 nuclear pact and improve prospects for social liberalisation and political pluralism.
However many Iranians are sceptical about his ability to fulfil his campaign promises as Supreme Leader Ayatollah Ali Khamenei, not the president, is the ultimate authority in the Islamic Republic.
"Dear people of Iran, the election is over, and this is just the beginning of our working together. A difficult road is ahead. It can only be smooth with your cooperation, empathy and trust," Pezeshkian said in a post on social media platform X, formerly known as Twitter.
"I extend my hand to you and swear on my honour that I will not abandon you on this path. Do not abandon me."
Turnout was almost 50% in Friday's vote, following historically low turnout in the first round ballot on June 28, when over 60% of Iranian voters abstained. The election was called after President Ebrahim Raisi was killed in a helicopter crash in May.
After a seven-year rupture, Saudi Arabia and Iran resumed relations under a surprise China-brokered deal announced in March last year.
Since then the two Middle East powers, which have often supported opposing sides in regional conflicts, have intensified their contacts.
Iran's ultraconservative Raisi travelled to Riyadh in November for a summit on the Israel-Hamas war in the Gaza Strip.
The emir of Kuwait, another Gulf state, also sent a cable of congratulations to Pezeshkian, wishing "more prosperity and development" for the Islamic republic, Kuwait's official KUNA news agency said.
