Exchange of fire
Israeli forces exchanged fire with gunmen in the camp, and militants said they also fired rocket-propelled grenades at the troops.
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Israeli aircraft attacked several Palestinian fighters who came close to troops during the raid, an Israeli military spokeswoman said.
Palestinian medics said two fighters were killed in the air raid and a Hamas television cameraman was wounded.
Palestinian medical workers said the bodies of three other Palestinian fighters arrived in hospital, apparently killed in the ground clashes.
An Israeli military spokeswoman said soldiers had carried out a "routine operation" about a kilometre inside Gaza to locate Palestinian fighters.
Nour Odeh, Al Jazeera's correspondent in Gaza, said: "Israel has given itself the right to maintain military operations within a certain distance from the border in the Gaza Strip, even two years after it said it completely left the [it].
"... That's why the Israeli military considers entry the peripheries of al-Barij refugee camp a routine operation."
The deaths bring to 5,776 the number of people killed since the outbreak of the second Palestinian uprising in September 2000, most of them Palestinians, according to a tally by the AFP news agency.
Israel withdrew from Gaza in 2005 after 38 years of occupation, but continues to carry out armed incursions and air strikes in the territory from where Palestinian fighters fire rockets into Israeli territory.