(This April 23 story was corrected to clarify source for number of displaced people)
By Ahmed Aboulenein
MOSUL, Iraq (Reuters) - Heavy two-way traffic of carts carrying children, clothes, and the elderly crowded the main Baghdad-Mosul road on Sunday as hundreds of Iraqis fled heavy fighting or made their way back to areas seized back from Islamic State.
Families paid no heed to the sound of heavy mortar, artillery and machine gun fire raging in the background as U.S.-trained Iraqi forces battled Islamic State some two km.(about a mile) away.
Some had walked miles to a government checkpoint where the men were placed in army trucks and sent for security screening to ensure no militant sleeper cells get out of the city. Women and children were put on busses and sent to camps housing hundreds of thousands, some displaced since the offensive to retake the Islamic State stronghold began in October.
"We left because of darkness, hunger, and death. There are bullets and air strikes. We were injured, our children were injured," said Younnes Ahmed, who was fleeing al-Thaura district with his family, their clothes all piled on a cart. There was a deep bullet wound on his hand.
A group of young men further inside the city sat on the street as soldiers gave them back identification cards they had taken to conduct background checks before letting them go.
Most houses were reduced to rubble, either because of air strikes or Islamic State bombs. Cars were hollowed out.
"Islamic State blew up my house with TNT to shield against air strikes," said Hossam Saleh who now lives in rubble because he has nowhere to escape to.
Others were walking back into the city, eager to reclaim their homes after their neighborhoods had been retaken from Islamic State by U.S.-backed security forces.
"We left because of the air strikes but have now returned. But we want the government to restore services like electricity and water and to allow us to drive instead of using carts," said Mosaab Mohamed who was walking back into Mosul with his family.
Iraqi forces have taken much of Mosul from the militants who overran the city in June 2014. The military now controls the eastern districts and are making advances in the west.
Islamic State fighters, holding out in the Old City, are surrounded in the northwest and are using booby traps, sniper and mortar fire to defend themselves.
Three policemen were killed in a suicide attack south of Mosul. A group of about 10 assailants, including four suicide bombers, had tried to infiltrate a Federal Police helicopter base in Al-Areej, a police captain told Reuters.
Those who have returned say the government has been slow to restore services even to western districts that had been retaken a while ago.
"We are besieged in the Resala area. There are stray bullets from other areas where there is fighting; three children have died," said Mohamed Sobhi.
"Water and aid cannot reach us. I call on the government to redistribute the people in areas like ours into other safer areas in Mosul."
Hundreds of thousands of civilians are still trapped in western Mosul, where Iraqi forces are making slow progress against Islamic State in what is a labyrinth of narrow streets.
As of April 20, some 503,000 people have been displaced from Mosul since October, according to government figures provided by the U.N. refugee agency UNHCR. The U.N. migration agency, the IOM, puts the displaced figure at 334,518 people as of April 23.
Still, there were signs of a slow return to commerce on Sunday, with one man setting up a cigarette stand and a family selling candy bars and water on the Mosul-Baghdad road, and residents were eager to rebuild.
"We do not want anything from the government, we just want to be allowed to help ourselves. If we can have letters allowing us to go other places we will get our own water, and transport it back," said Omar Khaled as he carried his infant son back into the city.
(Reporting by Ahmed Aboulenein; editing by Ralph Boulton)