The U.S. military said on Monday it had killed 22 fighters who attacked an Iraqi checkpoint in northeastern Baghdad.

The military said in a statement the fighters had attacked the Iraqi Security Force checkpoint on Sunday.

It said U.S. soldiers had killed "the 22 criminals, forcing remaining enemy forces present to retreat.

"The criminals' small-arms fire was ineffective and there were no U.S. or ISF casualties in the attack," the military added.

Militants bombarded Baghdad's Green Zone with rockets on Sunday, taking advantage of the cover of a blinding dust storm to launch one of the heaviest strikes in weeks on the fortified compound.

The strikes appeared to defy a renewed call for a ceasefire by Shi'ite cleric Moqtada al-Sadr, which has seen many of his masked gunmen leave the streets of the Sadr City slum where they hold sway in eastern Baghdad.

Reuters correspondents heard the missiles whistling overhead and exploding inside the heavily fortified government and diplomatic compound on the west side of the Tigris River in Baghdad. Sirens wailed, ordering people to take cover.

Iraqi police said eight missiles or mortars had hit the Green Zone and another 14 fell in other parts of the Iraqi capital before nightfall in several quick bursts, killing two people and wounding 20.

"The Green Zone has received several rounds of IDF (indirect fire) but I can't say more than that," U.S. embassy spokesman Armand Cucciniello said. "The duck and cover alarm sounded and people ran out for cover."

Several more missiles were fired late on Sunday evening but it was unclear if there were any casualties.

The United States blames rogue elements of Sadr's Mehdi Army militia for firing the rockets. It accuses neighbouring Shi'ite Iran of supplying the weapons and says some were made as recently as last year. Iran denies the accusations.

Militiamen have fired 700 missiles and mortars over the past month in Baghdad, but U.S. forces had said they believed they had reduced the fighters' ability to strike the Green Zone by occupying the part of the Sadr City slum closest to it.