On Monday, US Defense Secretary Mark Esper "expressed his concern" over the strikes in a telephone call with outgoing prime minister Adel Abdel Mahdi, according to a statement from the premier's office.
In response, Abdel Mahdi "called on everyone to spare no effort to prevent an escalation that will threaten all parties", the statement added.
"Unilateral decisions will trigger negative reactions that will make it more difficult to control the situation and will threaten Iraq's security, sovereignty and independence," he said.
Abdel Mahdi resigned in early December after the two months of unprecedented demonstrations in the capital and south in which around 460 people have died.
Negotiations are underway to name his successor.
"If the Iraqi government or state weakens, this will exacerbate escalation and chaos," Abdel Mahdi told Esper, according to the statement.
US officials say they are considering sending 5,000 to 7,000 troops to the region, although Esper on Friday again denied a report that a 14,000-strong deployment was under discussion.