Gabriel published a Twitter message congratulating Rouhani and interpreted Iranians vote for him as wholehearted support for political and economic opportunities. Some said the pattern was all too familiar from Rouhani's first victory four years ago and Khatami's victories the previous decade.
Rouhani also underlined that he is "the president of the entire Iranian nation, even those who have opposed my policies", extending a hand of help and friendship to all of the country's people. It is expected he will express his gratitude for the overwhelming support of the more than 56 million Iranians who voted on Friday. But neither presidential candidate Donald Trump's vows to "tear it up" nor Iranian critics' promises have come to fruition.
Over 1.1 million votes have been found invalid thus far. Iran's president is one of three members on a temporary council that takes over the supreme leader's duties should his post become vacant until a successor is named by the panel known as the Assembly of Experts.
But the deal has serious opponents in the U.S., where President Donald Trump and the Congress are reviewing their options.
The re-elected President will have to navigate a tricky relationship with Washington, which appears at best ambivalent about a nuclear accord agreed by former President Barack Obama.
Oil sales have rebounded since the nuclear deal took effect in January a year ago, but growth in the rest of the economy has been limited, leaving unemployment at 12.5 percent overall, and at nearly 30 percent among young people.
Interior Minister Abdul Reza Rahmani Fazli said Raisi received 38.5%, or 15.7m votes - not enough to take the election to a second round.
He also picked a rare public fight with hardliners close to Supreme Leader Ayatollah Ali Khamenei, angrily criticising their favourite in the race, Mr Ebrahim Raisi, a judge seen by reformists as representing the security state at its most fearsome.
Hashemitaba was among the first to predict an outright win for Rouhani as he offered his congratulations Saturday morning.
That gave hope to his supporters, who during recent campaign rallies called for the release of two reformist leaders of the 2009 Green Movement who remain under house arrest. His administration said it put Iran "on notice" in February after issuing a series of sanctions following ballistic missile tests. Trump made a decision to do so, but also imposed narrow sanctions against two Iranian defense officials and an Iranian company that the USA government said were linked to Iran's ballistic missile program.
Ahmadi said the Interior Ministry expects to announce final results later Saturday.