DUBAI, May 29 (Reuters) - The al Qaeda-led Islamic State in Iraq group on Tuesday criticised as satanic talks between Iran and the United States in Baghdad. The United States and Iran held their most high-profile meeting in almost 30 years on Monday. The meeting between the arch-foes at ambassador level in the Iraqi capital was called to discuss ways of ending the conflict in Iraq. The Islamic State in Iraq, led by Sunni Arabs, said in a statement posted on the Internet that Shi'ite Muslim Iran was willing to abandon its nuclear programme to win U.S. blessing to dominate Iraq, which has a Shi'ite-led government. "The Great Satan and its allies sat together to conspire against the people of Islam (Sunnis) after the projects of the crusaders and the Shi'ites reached a dead end," said the group. Iranian officials and clerics often describe the United States as the "Great Satan". The meeting marked a shift in the U.S. policy of shunning almost all contact with Iran since severing diplomatic ties in 1980, 14 months after Iran's Islamic Revolution and five months after Americans were seized in a hostage crisis in Tehran. It did not touch on Iran's controversial nuclear programme. Washington accuses Iran of trying to build a nuclear bomb, but Tehran says its programme is only for generation of electricity. "Each side found the other as a bridge to reach their respective goals," said the Islamic Group in Iraq. "The bargain would be over the nuclear file in return for official recognition of Iran's influence in Iraq ... so that the killing of Sunni people becomes legitimate." Iraq has been plagued by sectarian violence between the Shi'ite majority and the Sunni Arab minority, once dominant under Saddam Hussein.