"We are waiting for the new government to find stability and continuity in its policies", said Rouhani.
He also criticised U.S. president Donald Trump's visit to Saudi Arabia, describing it as a "show-off" that "will not have any political and practical values".
Rouhani, a 68-year-old moderate cleric who spearheaded a 2015 nuclear deal with world powers, said Iranians had chosen the "path of engagement" and rejected extremism after he took 57 percent of the vote against 38 percent for hardline cleric Ebrahim Raisi.
"We didn't leave Mashhad, we took it back", chanted young people in Raisi's hometown and one of the centres of Shia Islam in Iran.
Heshmat Alavi, a human rights activist, wrote an op-ed for Al Arabiya, in which he assessed that following Rouhani's're-election', the most important issue was ending Iran's destructive influence on the Middle East.
Police tried to disperse people in central Vali Asr Square, saying they did not have a permit to assemble, but the crowd was too large to manage.
Trump has repeatedly described it as "one of the worst deals ever signed", although his administration re-authorised waivers from sanctions this week.
Rouhani also criticised Iran's arch-foe Saudi Arabia over its lack of democracy, urging Riyadh to allow its people to decide their country's fate through free elections.More news: Google Is Building a New Virtual Reality Headset
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"The fact that Rouhani won as a reformist who delivered the nuclear deal and promised to bring in foreign investment would suggest that there is support for things like the oil contracts", Patrick Murphy, a Dubai-based partner at law firm Clyde & Co., said by phone Sunday.
Despite the lifting of sanctions, large global banks have avoided doing business with Iran, after regulators in the USA fined many of them billions of dollars for continuing to deal with the country when sanctions were in place.
The Sunni kingdom and Shiite power Iran haven't had diplomatic relations since early 2016. The Gulf Arab state a year ago downgraded ties with Tehran after Saudi Arabia severed ties with Tehran after demonstrators angry at the execution of a Shi'a Muslim cleric in the kingdom attacked Saudi missions.
They repeated the trick at the weekend, taking all 21 council seats in the capital and displacing the conservatives for the first time since 2003.
Speaking after moderate President Hassan Rouhani's re-election, an Iranian trade minister said the country needs major investments for offshore oil and gas.
Rouhani did point out, however, that "the world fully understands that Iran is now in the path of interaction with the worldwide community and minds to promote peace and friendship, but it will not accept humiliation under any circumstances". "We expect Iran to behave responsibly. not to support terror", said his German counterpart Sigmar Gabriel.
At the Tehran press conference, Rouhani also defended Iran's ballistic missile program, something heavily criticized by the Trump administration. "Our missiles are for peace and for defence", he said.