The official Falah al-Dirmani said the casualties were taken to hospitals in the city, 170 km southeast of Baghdad.
US planes started bombing the al-Shakia district, in southern Kut after 3am (2300 GMT Wednesday) on Thursday, said Kut hospital director, Khadir Fadal Arar.
Many of the dead and wounded were women and children, he added.
The bombardment followed a day of fierce clashes between Iraqi police and fighters of the Al-Mahdi army loyal to Shia leader Muqtada al-Sadr, in which at least two national guardsmen and three policemen were wounded.
The office of al-Sadr's movement in Kut was flattened in the bombing, said his supporter, Shaikh Muhammad Yihyiah.
Al-Mahdi fighters blocked streets
of Kut and the governor's office
"Our office has been destroyed because it was in the same district, fortunately there were was no one in the office that's why we have no casualties. Perhaps they thought it would be full of fighters," he said.
On Wednesday, Iraqi police and security forces were locked in clashes with fighters who attacked Kut's city hall, police stations and national guard barracks, said a statement from the Polish-led occupation force in the area.
The occupation force said people on both sides were killed and wounded, but did not specify a casualty toll.
Al-Mahdi Army fighters had blocked off streets and besieged the governor's office in the eastern part of the town, armed with Kalashnikovs and rocket-propelled grenades, as US planes flew overhead.
Governorate spokesman Majid Hamid said a written death threat had been delivered to the province's governor because he had refused to bow to demands from al-Sadr supporters that Kut secede from Iraq with other Shia provinces of the south and centre.
"... fortunately there were was no one in the office that's why we have no casualties"
Shaikh Muhammad Yihyiah,
The occupation force in the area has "increased its combat readiness" and is prepared to support the Iraqi security forces," said a statement from the Polish-led military issued late on Wednesday.
Kut fell briefly to the Al-Mahdi army in the spring during al-Sadr's first clash with occupation troops.
One killed in Ramadi
Ramadi has seen heavy clashes
between fighters and US troops
One civilian was killed and two were wounded on Thursday when fighters ambushed a US occupation military convoy in Ramadi, a medic said.
One of the two injured is serious, while one person was killed in the ambush, doctor Muthana Hindi of Ramadi general hospital said.
The US convoy was ambushed at around 9:00 am (0500 GMT) by fighters and the fire exchange between the two lasted for nearly two hours.
Meanwhile, a car bomb exploded on Thursday as a US occupation convoy passed through al-Warwar bridge at the western gate of Ramadi city, reported our correspondent.
More details were not immediately available.
Ramadi, 100 km west of the capital Baghdad, is the site of frequent clashes between fighters and US occupation forces.