Speaking to world leaders at the UN General Assembly, George Bush also urged Iran to return immediately to international talks on its nuclear programme.
"My country desires peace," Bush said.
"Extremists in your midst spread propaganda claiming that the West is engaged in a war against Islam. This propaganda is false and its purpose is to confuse you and justify acts of terror. We respect Islam."
Bush spoke to Iraq directly, saying, "we will not abandon you in your struggle to build a free nation."
Mahmoud Ahmadinejad, the Iranian president, was scheduled to speak to the body later on Tuesday, but he was not at the country's table in the hall when Bush spoke.
Speaking to Iranians, Bush said their country's future has been clouded because "your rulers have chosen to deny you liberty and to use your nation's resources to fund terrorism and fuel extremism and pursue nuclear weapons."
The US and other countries fear Iran is trying to build nuclear weapons, while Tehran insists its uranium enrichment programme is solely for civilian purposes.
Bush delivered strong warnings to both the United Nations and the Sudanese government on the violence in its Darfur region. He said both UN and the Sudan must act now to avert a further humanitarian crisis.
Bush said that if the Sudanese government did not withdraw its rejection of a UN peacekeeping force for Darfur, the world body should act over the government's objections.
"The regime in Khartoum is stopping the deployment of this force," Bush said. "If the Sudanese government does not approve this peacekeeping force quickly, the United Nations must act."