Four US soldiers have been killed along with scores of militants following two days of fighting in the Baghdad slum of Sadr City and rocket fire elsewhere in the capital.

The latest casualties, announced yesterday, make April the deadliest month in Iraq for the US military since last September, with at least 44 soldiers dying, according to a toll by the Associated Press.

Casualties had declined in recent months in line with a sharp drop in violence. But attack levels have rebounded slightly in the past few weeks as Iraqi and US forces push into the Shia militia strongholds of Sadr City in Baghdad and Basra in the south of the country.

A rocket or mortar attack in east Baghdad killed three US soldiers yesterday. The US military did not give an exact location of the incident, but Sadr City lies to the east. The fourth serviceman was killed by a shell in the west of the capital.

The deaths came as US troops said that they killed 45 Shia militiamen in fierce fighting over the past two days that included a tank battle with dozens of gunmen who attacked a checkpoint under cover of a dust storm.

The checkpoint attack on Sunday night sparked the biggest battle in Sadr City since Nouri al-Maliki, the Prime Minister, cracked down on militias a month ago, with 22 gunmen dying in the assault. Another 23 were killed in other battles over the past two days in and around the slum district.

The fighting indicated that some members of the Mehdi Army, the most powerful Shia militia in Iraq, have apparently defied an order by Moqtada al-Sadr, the radical cleric who supposedly controls the militants, to observe a ceasefire.

In a further sign of hostility, a barrage of at least three more mortar or rocket attacks hit the fortified Green Zone yesterday, sending American, British and other foreign officials scurrying for cover. There were no reports of injuries.

US forces are pushing into Sadr City, from where many of the rockets directed at the Green Zone are launched, to prevent militants from launching the missiles.

Thirty Iraqi lawmakers from various political parties yesterday however urged Mr Maliki to end the month-long confrontation, saying innocent civilians and children were the main victims of the fighting.

“Yes, you can do it if you remember your own children,” said a joint statement read by Mustafa al-Heeti, a Sunni Member of Parliament. “Your people are demanding of you to intervene and solve the crisis peacefully.”

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