The violence, which began on May 20, has caused severe power shortages across the country in recent weeks as ships have been unable to deliver oil to the Deir Ammar plant.
Eid said one of the rockets struck near one of the reservoirs, causing a fire but it was quickly put out.
A building was hit by another rocket while the other three landed in the grounds of the facility.
The power station was shut down after the attack.
Witnesses reported that there were fierce clashes between the military and fighters still holed up inside the camp on Thursday morning.
More than 200 people have been killed, including 124 Lebanese soldiers, since the army began battering the refugee camp with artillery and tank fire more than two months ago.
"The fighting will continue until this [Fatah al-Islam] phenomenon is eliminated," an official said.
The four Fatah al-Islam fighters were killed on Wednesday when they attacked a military unit, the NNA said.
Last week, Lebanese troops stormed a hideout of Fatah Islam fighters in the camp, killing eight of them, according to the news agency.
General Michel Suleiman, Lebanese army commander, has vowed to continue the battle saying it was a "fight against terrorism" and "a battle of dignity and national sovereignty".
In a speech during Wednesday's Army Day, he called the military deaths in the Nahr al-Bared "great sacrifices".