Iraq's Shi'ite-led government, one of the few in the world to maintain close military and diplomatic ties with both Tehran and Washington, called an emergency meeting. The prime minister's office urged the parties involved to avoid escalation, adding that it wanted to keep the country out of regional conflicts.
The Iraqi presidency denounced the strikes on the paramilitaries as "an unacceptable attack and a flagrant violation of Iraq's sovereignty", while also calling for a halt to attacks by armed groups against Iraq's neighbours.
Trump told Fox that the United States had coordinated with the Iraqi government in launching the attacks. Baghdad did not specifically address Trump's suggestion it had cooperated, but said only its government has the authority to respond to attacks on its territory.
Iran said the U.S.-Saudi attacks were an attempt by the United States and Israel to spread their war further in the region. One of the Iran-backed armed groups in Iraq, Harakat Hezbollah al-Nujaba, said U.S. and Saudi forces would pay a "heavy price".
Washington has long called on the Baghdad government to crack down on Iran-backed paramilitaries, but efforts to do so in the past have provoked domestic unrest.
The deep ties between Iran and Iraq, the two biggest Shi'ite-majority countries, are heightened this week as hundreds of thousands of Iranian religious pilgrims head to shrines in Iraq for an annual day of mourning for martyrs. Some carried portraits of Iran's slain Supreme Leader Ayatollah Ali Khamenei.
Saudi Arabia has also been drawn into the conflict on another front, with the Iran-aligned Houthi movement in Yemen announcing a blockade of Saudi oil exports in the Red Sea last week and firing on ships and oil facilities. The Houthi group is considering imposing fees on commercial ships transiting the sea, sources with knowledge of the matter told Reuters.
Hours before launching the joint attacks with Saudi Arabia on Iraq, the U.S. military said its air defences had averted a surprise Iranian attack on U.S. troops in the region.
Jordan's military said it had shot down five Iranian missiles. U.S. bases in Jordan have lately become primary Iranian targets, where three U.S. service members were killed this month in the worst U.S. losses since March.
Iran's Revolutionary Guards said they had fired several ballistic missiles at U.S. military installations in Jordan, and had struck three tankers that were attempting to transit through the Strait of Hormuz along an unauthorised route.