The fighting with machine guns and mortars raged around the stronghold of the Hilles clan, which is allied with Hamas rival Fatah. Loud explosions could be heard throughout Gaza City, and ambulances and police cruisers raced to the scene.
The six Hamas policemen were in a critical condition, a police spokesman said. He also reported 15 arrests.
It was the most violent confrontation between Hamas forces and Fatah supporters since last week's deadly bombing, in which five Hamas militants and a six year-old girl were killed in a beachside attack.
Hamas blamed Fatah and arrested more than 200 Fatah supporters in the toughest crackdown since seizing Gaza by force last year. The group said the clan is hiding bombing suspects. The clan denies the charge, and said it would defend its homes.
"You have to decide: Either be trampled under Hamas' shoes, or stand in dignity," said Ahmad Hilles, a Fatah leader and a senior clan member to The Associated Press as gunfire crackled in the background. He said Hamas cut electricity.
Hamas police spokesman Islam Shahwan said suspects in last week's bombing were believed to be hiding in the clan's compound in the Shijaiyeh district. During the fighting, a rocket hit members of a family, wounding several people, Shahwan said.
Shahwan claimed three Hilles men were seen fleeing the area, disguised as women. He said Hamas security men stormed several high-rise buildings and arrested rooftop snipers, gunmen and wounded fighters.
"We are determined to continue the raid until we arrest all those involved," Shahwan said. "This is just the beginning," he said.
As fighting continued, Hamas officials shut down a radio station affiliated with the small Popular Front for the Liberation of Palestine, saying that the station was reporting "lies and rumors and inciting sedition," the group said.
Meanwhile, in the West Bank, ruled by Fatah, security forces searched cars at checkpoints in northern cities, checking identification cards. Dozens of Palestinian Authority security men toting AK-47s patrolled Nablus, a Hamas stronghold.