"We call on the Government of Iraq to fulfill its obligations to protect our diplomatic facilities," a State Department spokesperson said in a statement.

The attack marked a dangerous escalation in a spree of rocket attacks in recent months that have targeted the embassy or Iraqi military bases where American troops are deployed.

None of the attacks has been claimed, but Washington has repeatedly blamed Iran-backed military factions in Iraq.

On Sunday, one rocket hit an embassy cafeteria at dinner time while two others landed nearby, a security source told AFP.

"Since September there have been over 14 attacks by Iran and Iranian-supported militias on US personnel in Iraq," the State Department spokesperson said.

"The security situation remains tense and Iranian-backed armed groups remain a threat. So, we remain vigilant."