Reporters in Tehran for the New York Times and the Washington Post both said on Twitter that they could access the service freely on Monday.
Jillian York, the director for international freedom of expression at the Electronic Frontier Foundation, a civil liberties organization, said she had received multiple reports from citizens using several different Iranian Internet service providers confirming that the bans appeared to have been lifted.
"Some other blocked sites are reporting themselves unblocked - the National Iranian American council is reporting themselves unblocked as well," York said, referring to a US-based nonprofit group.
Iranian authorities blacked out Facebook and Twitter in the summer of 2009, when Ahmadinejad's disputed re-election victory sparked massive protests that gained momentum with the help of organizers using social media.
The administration of the new president, the moderate cleric Hassan Rouhani who took office last month, has signaled - on social media, no less - that it will adopt a much different tack from that of its hardline predecessor.
Marking the Jewish New Year earlier this month, Rouhani and Foreign Minister Javad Zarif wrote on their Twitter accounts to wish Jews a happy Rosh Hashanah.
No Iranian government statement about loosening the restrictions was reported on Monday.