Ali Larijani, the secretary of Iran's Supreme National Security Council, told reporters on Thursday that any talks between the United States and Iran would be limited to Iraqi issues.
Larijani, who is also Iran's top nuclear negotiator, said Zalmay Khalilzad, the US ambassador to Baghdad, had repeatedly invited Iran for talks on Iraq.
In Washington, White House spokesman Scott McClellan said Khalilzad was authorised to talk to the Iranians about Iraq just as the United States had talked to Iran about Afghanistan.
"This is a very narrow mandate dealing specifically with issues relating to Iraq," McClellan said, adding that it did not include US concerns about Iran's nuclear programme.
Any direct dialogue between Tehran and Washington could be the beginning of negotiations between the two old foes over Iran's nuclear programme.
Washington accuses Iran of trying to build nuclear weapons and is leading a campaign for UN Security Council action. Iran denies the accusation but wants to avoid any penalties from the Security Council, which is expected to discuss Iran's nuclear programme this month.
The United States also accuses Iran of meddling in Iraqi politics and of sending weapons and men to support the insurgency.
Iran is accused of helping
militias in Iraq
"To resolve Iraqi issues, and to help the establishment of an independent and free government in Iraq, we agree to (talks with the United States)," Larijani told reporters after a closed meeting of the parliament.
His statement was the first time since the 1979 Islamic Revolution that Iran had officially proposed dialogue with the United States, which many of its top officials still refer to as "the Great Satan".
Analyst Davoud Hermidas Bavand, a professor of international relations at Tehran's Imam Sadeq University, said Larijani's call was a genuine offer that could have significant consequences.
"This could be the beginning of a major breakthrough, ending more than two and a half decades of estrangement between Tehran and Washington," Bavand said.
Bavand said that some of the clerics within the ruling establishment are convinced that Iran will be harmed by a head-on collision with the world over its nuclear activities.
How much support such views enjoy is unclear because the ruling establishment is opaque, but it is known that there are clerics who disagree with the foreign policies of Mahmoud Ahmadinejad, the Iranian president, who takes a hard line against dialogue with the United States.
"Iran is ready to use its Iraq card to protect its nuclear achievements before it is too late"
Bavand said that after Iran's nuclear programme was reported to the UN Security Council last month, Russia and China sent messages to Iran saying that if it wanted a face-saving solution, it had to talk to America.
"Iran needs America to calm the growing tension over its nuclear programme," Bavand said. At the same time, Washington wants to restore stability to Iraq, "and Iran has sufficient weight and influence to help it out".
Another political analyst in Tehran, Saeed Leylaz, also said that Tehran would be prepared to trade progress on Iraq with movement on the nuclear issue by Washington.
"Continued instability in Iraq is hampering America's plans for the Middle East. Iran is ready to use its Iraq card to protect its nuclear achievements before it is too late," Leylaz said.
Donald Rumsfeld, the US defence secretary, recently accused Iranian Revolutionary Guards of assisting the smuggling of explosives and bomb-making material into Iraq.
Iran denied the US charges, saying the occupying forces were responsible for the instability in Iraq.
But Iran has expressed concern about the violence in Iraq, where sectarian fighting and reprisal killings have escalated recently.