Foreign ministry spokesman Hamid Reza Asefi, speaking at a press conference on Sunday, said the situation in Iraq is "serious and this is why we have addressed the necessary warning".
Washington has no diplomatic relations with Tehran and the warning was passed by diplomatic channels through the Swiss embassy in Tehran, which represents US interests in Iran.
Shia-dominated Iran has voiced alarm in recent days at fighting around the Shia holy cities of Najaf and Karbala between US occupation forces and followers of Iraqi Shia leader Muqtada al-Sadr's al-Mahdi Army.
Iran opposed the US-led invasion of Iraq, with which it fought a bloody war from 1980 to 1988 that left hundreds of thousands killed, and has called for an end to the occupation.
Violent demonstrations have been staged recently outside the British embassy in Tehran against the actions of the US and its main ally Britain in Iraq.
"We want several things for Iraq, the most important of which are the departure of the occupation forces as quickly as possible and the restitution of authority to the Iraqi people themselves," Asefi said.
The US accuses Iran of influencing Iraq's Shia population to destabilise the country, and allowing foreign fighters to cross its borders into Iraq. Tehran denies the accusations.