Twitter, on its official blog, said some of its records had been temporarily compromised but the problem had been fixed and it would investigate.
The popular microblogging site was apparently disrupted for about two hours by the group, which replaced the Twitter home page with a headline reading This site has been hacked by Iranian Cyber Army and with an anti-American message.
A screen shot posted in a number of places on the web, including TechCrunch, shows the message written in red, set above a green flag.
Twitter did not immediately respond to email requests for an interview. An email sent to the address on the redirected web page was returned.
Twitter, which allows people to broadcast short, 140-character text messages over the web, has found itself caught up in Iranian politics before. In June, it became a key form of communication in Iran amid the protests and clampdown that followed the country's disputed June elections.
At the time, the U.S. State Department urged Twitter to delay maintenance that would have interrupted the site's service during the peak of the demonstrations.
James Lewis, a cybersecurity effort with the think tank Center for Strategic and International Studies, said Thursday's attack may have come from a group supportive of the government, but not part of it.
This is ham handed so it's probably not the Iranian government. It could be sympathizers, said Lewis, who said the government would have been more likely to hack Twitter during protests or other upheaval when the site was being used by dissidents.
(Reporting by Paul Thomasch in New York, Diane Bartz in Washington, and A.Ananthalakshmi in Bangalore; Editing by Lisa Von Ahn and Steve Orlofsky)
(Reporting by Paul Thomasch)