BAGHDAD, Iraq (CNN) -- Shiite militants and U.S.-backed Iraqi forces -- two sides that agreed to a cease-fire last week -- fought overnight in Sadr City, killing four people and wounding 38, Interior Ministry and hospital officials said Sunday.
A spokesman for radical cleric Muqtada al-Sadr said the fighting does not mean an end to the newly negotiated peace agreement.
Neither side agreed on what caused the fighting in the stronghold of al-Sadr's Mehdi Army militia.
Major Gen. Qassim Atta, a Baghdad security plan spokesman, said "outlaw groups" using various weapons attacked Iraqi army checkpoints in the heart of Sadr City, a densely populated Shiite neighborhood in Baghdad. Iraqi forces returned fire, he said.
Al-Sadr spokesman Sheikh Salah al-Obeidi dismissed Atta's account, claiming that Iraqi security forces provoked people in an outdoor market by cursing at them. Iraqi forces were the only shooters, al-Obeidi said.
The incident killed seven Iraqis, including three children, al-Obeidi said.
Atta did not provide casualty figures.
Also on Sunday, a U.S. soldier was killed in a roadside bomb attack in Iraq's Salaheddin province, the U.S. military said. The bomb struck a vehicle carrying Multi-National Division-North soldiers, wounding one other soldier, the military said.
The death brings Iraq war casualties U.S. military personnel to 4,079. Fourteen have been killed so far this month. Salaheddin province is about 100 miles (160 kilometers) north of Baghdad.
Al-Obeidi, the Al-Sadr spokesman, said the Sadr City peace agreement still holds. Despite "a major violation" by security forces Saturday, "such violations do not mean an end to the agreement," he told CNN Sunday.
Al-Obeidi said meetings between the two sides are ongoing, and this incident and punishment of those responsible will be addressed. One of the aims of the deal was to impose a four-day cease-fire and get troops into the district a few days later to impose law and order, clear bombs and collect weaponry used by militias.
U.S. military officials released a statement saying there were two violent clashes in Sadr City overnight. One of them involved Iraqi soldiers, and the other involved coalition forces or U.S. soldiers. The incident involving U.S. soldiers resulted in U.S. soldiers killing "four criminals" who returned fire at a security checkpoint, the statement read.
It is unclear if the four fatalities in the U.S. military press release are the same four people that the Iraqi interior ministry official identified.
The Iraqi army entered Sadr City on Friday and had started removing roadside bombs, Atta said last week.
Fighting had started in Sadr City in late March after a government offensive in the Shiite city of Basra against "outlaw" elements. That offensive sparked animosities throughout the Shiite heartland, and the fighting spread to Baghdad.
Much of the fighting involved the Mehdi Army and Iraqi security forces, which were dominated by members of the Sadrists' rival -- the Islamic Supreme Council of Iraq. The U.S. military has supported the Iraqi military and police.
Last week, the Sadrists and the United Iraqi Alliance -- a powerful political bloc that includes the Islamic Supreme Council of Iraq -- worked out a deal to end the fighting.
In the southern city of Basra, oil exports dropped about 2 million barrels in one month because of fighting between Iraqi security forces and Shiite militiamen, an official with Iraq's Oil Ministry said Sunday.
The official said that oil exports in April were about 57 million barrels, down from 59 million in March. The official said the country usually exports oil from three ports: two in Basra and one in southern Turkey. This effort has been hampered by fighting, the official said.
In early April, fighting in Basra between Iraqi security forces and Shiite militias damaged some pipelines and forced the shutdown of some units, the official said.
CNN's Mohammed Tawfeeq and Jomana Karadsheh contributed to this report.