The shelling began at 6am (0300GMT) on Friday after a pause overnight.
"They are pounding positions and we are hearing a lot of gunfire suggesting that there may some clashes with Fatah al-Islam continuing to respond," Zeina Khodr, Al Jazeera's correspondent outside the camp, said.
"The army seems intent on advancing towards the old sector of the camp where the remaining Fatah al-Islam fighters are believed to be in hiding and fortifying their positions."
The civilian was killed by a stray bullet on a main road outside the camp.
The soldiers were killed by shrapnel or sniper fire, military officials said.
'Tightening the noose'
The Lebanese army has denied that the bombardment was part of a final assault on the camp.
"The current ongoing military operations are still in the framework of tightening the noose on the gunmen to force them to surrender and submit to justice," it said in a statement on Thursday.
Fouad Siniora, the prime minister, has called for the army to "put a final end" to the Fatah al-Islam "terrorists" holed up inside the camp.
Security and political sources said that the army had deployed extra troops in the area and was expected to use helicopter gunships and naval boats as well as tanks and heavy artillery in any assault on the camp.
The camp, which has run short of fresh food and water, has been largely deserted since almost all of its population of 31,000 people fled.
Relief workers have been unable to get supplies into the camp since June 20, forcing remaining residents to scavenge for food and water in abandoned houses.
More than 170 people have been killed during the 55 days that the camp has been under siege from the Lebanese army.
The fighting erupted when Fatah al-Islam fighters launched a string of attacks on soldiers, killing 27 of them around the camp and in nearby Tripoli, according to the military.