Majak Machar, a resident of the camp in Soba Aradi, about 30km south of Khartoum, said: "The troops, army and police came in this morning and they shot at the civilians."
"They wanted to take the people to another area, and the people fought them because they didn't want to go."
Slums and camps surrounding the sprawling capital are home to more than two million people from all over Sudan, but most of them are southerners who have fled two decades of civil war.
One eyewitness said residents of Soba Aradi had burned down the local police station and killed the officer in charge, who was from the south of Sudan.
"The people said we will not go, we will die here in Soba Aradi," Father Darwing, a local community leader, said. "They have been living there for 14 years."
Witnesses said the displaced people had taken guns from the police and returned fire.
An Interior Ministry spokesman said 11 policemen had been killed.
The United Nations said they had sent representatives to the area to try to calm the situation.
The governor of Khartoum was not immediately available to comment on the clashes.
One UN official at the scene said hundreds of people were fleeing the fighting. "It is not possible to move around inside still," the UN official said.
The slum areas around Khartoum have little or no running water or electricity, and aid agencies have found it difficult to fund assistance to them.
"They wanted to take the people to another area, and the people fought them because they didn't want to go"
a refugee camp resident
Khartoum authorities say they want to demolish the slums to relocate residents to permanent, planned housing plots.
But the UN has criticised the policy, saying the relocations of the residents are not carried out in consultation with the people, and they are moved to desert areas miles out of the capital where there are no services.
The governor of Khartoum insists the relocations are done with the consent of the people and their leaders.