Two other officials, speaking on condition of anonymity, told The Washington Post that the missiles came directly from Iran.
The missiles landed near a U.S. consulate complex and damaged a local television news studio at around 1:30 a.m. local time, the Post reported. No one was killed or injured.
According to the BBC, the U.S. State Department denounced the attack as "outrageous."
Iraqi Prime Minister Mustafa Al-Kadhimi took to Twitter, calling the strike "an attack on the security of our people" and promising that Iraq's "security forces will investigate and stand firm against any threats."
Iran-backed Iraqi militia groups previously launched a wave of rocket and drone attacks against U.S.-aligned targets in Iraq and Syria in January. Per the Post, these strikes "did not cause casualties among U.S. service members and were clustered around the second anniversary of the U.S. decision to assassinate revered Iranian Maj. Gen. Qasem Soleimani."