"The prime minister received a telephone call from US Secretary of State Mike Pompeo," the press service said in a statement.
"On his part, the U.S. Secretary of State said the information they have confirms the Iraqi government's statement that its territory was not used to carry out this attack," Abdul Mahdi's office said in a readout of a phone call between the two.
Saudi Aramco's oil facilities - the Abqaiq oil refinery and an oil processing facility near the Khurais oil field - were attacked with drones on Saturday, causing major fires and partially disrupting oil production.
Although Yemen's Houthis claimed responsibility for the attacks, Washington suggested that the drones could have been launched from the territory of Iran or Iraq. Tehran dismissed the allegations, with Foreign Minister Javad Zarif calling them "maximum deceit". Baghdad responded by saying that Iraqi territory had not been used to carry out the attacks.
US Secretary of State Mike Pompeo on Sunday repeatedly blamed the attacks on Saudi Aramco's oil facilities on Iran, saying that there was "no evidence the attacks came from Yemen". US President Donald Trump, for his part, said that his country was "locked and loaded depending on verification" of the culprit it expects to receive from Saudi Arabia.