It may not always be an easy reach, though, with hardliners still deeply suspicious of social media for its central role in opposition protests after Ahmadinejad's disputed 2009 re-election. Facebook and other main sites are blocked. But Iran's legions of young and tech-smart cyber-surfers consistently find proxy servers and other methods to bypass the controls.
Some newspapers Monday speculated that Rouhani's push for government Facebook accounts might signal an easing of some of the Internet barriers.
Not so, replied Iran's chief Internet overseer. Gholam Hossein Mohseni Ejehei, head of the supervisory board on Internet content, said "it is not the time for lifting filters" on Facebook and other sites.
In another spat, some government officials also denied they had already opened Facebook accounts.
The Communications Ministry issued a statement denying the Shargh report that its head, Mahmoud Vaezi, was on Facebook. A news website, Khabaronline.ir, reported that the oil minister, Bijan Zanganeh, has no link to any Facebook page claiming to be his.
Other ministers, presumably heeding Rouhani's advice, posted official meeting schedules and bureaucratic tidbits on their pages.
"Fake pages on Facebook are going to be an Achilles' heel for the Rouhani administration," wrote pro-reform journalist Mahmoud Haghverdi on his Twitter feed. "This misuse is making it difficult for authorities to remove filters."
Such murkiness is nothing new in Iran's online realm.
Last week, a Twitter message posted under Rouhani's name offered salutations on the Jewish new year, Rosh Hashanah, to Iran's Jewish community and others around the world. Rouhani's aides later said the posting was not from the president.
Then, hours later, Foreign Minister Mohammad Javad Zarif acknowledged that he sent a similar message marking the Jewish holiday in what was interpreted as a small bid toward easing hostilities between his nation and Israel.
Iran's supreme leader, Ayatollah Ali Khamenei, issued a religious decree last year that called Facebook permissible if it was not used for "corrupting" purposes. Yet Khameni also has denounced the Internet as the vanguard of a Western cultural invasion what he calls "Westoxification" that hardliners believe undermines Islamic values.
Iran's ruling clerics have gone as far as ordering development of a closed system that would allow only state-approved Internet sites.
But Khamenei, too, is not completely absent from the Net. His office maintains an official site. A Facebook page and Twitter account also are widely believed to reflect his views. He has neither disowned nor claimed them, adding to speculation they serve as his unofficial voice.
In June, the Twitter feed khamenei.ir carried musings about Khamenei's boyhood desires to work out at a gym and the pleasures of mountain strolls. More recently, it included praise for Victor Hugo's "Les Miserables" as one of literature's masterpieces.
The foreign minister, Zarif, asked his Facebook followers not to steal his name and image for their posts.
"I will be thankful that you publish your viewpoints under your own name," he wrote. "I am only responsible for my comments."
Saeed Leilaz, a Tehran-based political analyst, believed Rouhani's moderate views will eventually lead to the lifting of some Internet restrictions.
"Rouhani learned about the power of the Internet on Iran's public opinion during his electoral campaign," said Leilaz. "Now they are trying to use it for their own aims."
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Murphy reported from Dubai, United Arab Emirates.
