The body of one anti-government fighter had been retrieved from Nahr al-Bared, he said.
At least 170 people, mostly soldiers and Fatah al-Islam fighters, have been killed in the fighting so far.
It is unclear how many civilians have died inside the camp as security forces are barred from entering Lebanon's 12 Palestinian refugee camps by a decades-old Arab agreement.
Saturday's deaths are the first military fatalities since Elias Murr, Lebanon's defence minister, declared in a TV interview on Thursday that Fatah al-Islam had been "crushed".
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He said the Lebanese army was concentrating on "clean-up" operations against Fatah al-Islam remnants, after 33 days of fighting.
The army said on Thursday it would not end the siege of the camp until the fighters surrendered.
Palestinian mediators held talks on Friday with Fatah al-Islam at the camp and were due to hold more talks over the weekend to find a solution acceptable to the army and Fatah al-Islam.
On Saturday, heavy artillery was fired into the camp where Fatah al-Islam fighters have retreated and have set up sniper outposts.
The fighters responded to the army bombardment with small-arms fire and grenades, security sources said.
Zeina Khodr, Al Jazeera's correspondent in Lebanon, said Fatah al-Islam fighters had gone further into the "old camp" after Lebanese army troops took control of its new sector on the outskirts of the overall camp.
She said that most of the civilians who remained in the camp were in the old sector, and were therefore at even greater risk after Fatah al-Islam entered it.
Shaker al-Abssi, leader of Fatah al-Islam, has not been accounted for, despite reports that he has been killed during the fighting.
|Artillery shelling sends up smoke from|
Nahr al-Bared camp on Saturday [Reuters]
At least 31,000 Palestinian refugees normally live in the camp, with most fleeing from the Lebanese army shelling to the nearby Beddawi refugee camp.
The battle for Nahr al-Bared is Lebanon's worst internal violence since the end of the 1975-90 civil war.
The army says Fatah al-Islam started the conflict on May 20 by attacking its posts.
Fatah al-Islam, whose forces are drawn from across the Arab world and which bears no relation to the mainstream Palestinian Fatah movement, says it is acting in self-defence.
Before the violence broke out, Lebanese security services had been investigating an alleged bank raid in Tripoli by Fatah al-Islam members.
Fatah al-Islam says it has no organisational ties to al-Qaeda but shares elements of its ideology.