The strikes were lifted at about the same time on the day Suleimani was killed last Friday in an American drone attack at Baghdad airport.
U.S. President Donald Trump on Sunday threatened to impose sanctions on Iraq, the second-largest producer in the Organization of the Petroleum Exporting Countries (OPEC), if U.S. troops were forced to withdraw from the country.
"They were planning something", he said of the Iranians.
"A war in the Middle East would only benefit Daesh and other terrorist groups".
More than a dozen ballistic missiles were fired at the military bases in Al Asad and Irbil. Assessment of victims and damage that is now taking place.
Iranian officials said Tehran did not want a war and its strikes "concluded" its response to Friday's killing of Qassem Soleimani, a powerful general whose burial after days of mourning was completed around the time of the missile launches.
He said: "As we evaluate the situation and our response, we will take all necessary measures to protect and defend USA personnel, partners, and allies in the region". The initial outlook, he said, was "So far, so good!" I will make a statement tomorrow morning.
The Indian government advised his citizens not to travel to Iraq.
Canada has about 500 soldiers in Iraq, most of whom are there to help train local forces to fight the Islamic State of Iraq and the Levant.
Apart from the issue of revenge for the assassination of General Soleimani, what matters now in the confrontation with the United States is that military action would not suffice, the Leader underlined.
How far is Iran willing to go for revenge?
Democratic presidential candidate Joe Biden said Iran's retribution proves that Trump is "dangerously incompetent". The Democratic party warned of escalation and said that "the world can not afford war".