The Iranian delegation, the first to visit Baghdad since former Iraqi President Saddam Hussein was ousted in April, was led by the head of the Gulf Department at Iran’s Foreign Ministry, Hussein Sadiqi.
Tehran has expressed support for the Governing Council, which first met on 13 July in what Washington described as a first step towards “democracy”.
While the Council can appoint people to work with the US occupying administration, US officials have veto power over its decisions.
Sadiqi issued a statement saying Iran was ready to help reconstruct Iraq and co-operate with the Governing Council.
He also voiced Iran’s desire to “open a new page in relations with Iraq after three decades of abnormal ties”.
Sadiqi met Ayatollah Mohammad Baqr Al-Hakim, leader of the formerly Tehran-based Supreme Assembly for Islamic Revolution in Iraq (SAIRI). The group is represented on the Governing Council.
Since its occupation of Baghdad, Washington has accused Tehran of interfering in Iraq, an allegation Iran categorically denies.
Iran and Iraq fought a bloody war from 1980 until 1988 that left hundreds of thousands of people dead.
Saddam Hussein enjoyed significant support from the United States during Baghdad’s war with Tehran, which had emerged as an Islamic Republic.