Minor clashes occurred at the camp on Monday afternoon, with one Fatah al-Islam fighter remaining there killed by the Lebanese army.
Zeina Khodr, Al Jazeera's correspondent in Lebanon, said the lone fighter had continued to hide in the camp after Fatah al-Islam launched an operation to break out on Sunday.
Khodr also reported that security forces arrested three suspected Fatah al-Islam members in towns close to the camp on Monday.
More than 300 people have died in over three months of fighting at the camp, making it Lebanon's worst internal violence since the end of the 1975-1990 civil war.
Fouad Siniora, Lebanon's prime minister, declared "victory over terrorists" on Sunday, hours after fighting ended.
Siniora said: "It is the greatest national victory for Lebanon over the terrorists in Nahr al-Bared.
|Siniora said that the army had scored a|
'victory' over Fatah al-Islam [AFP]
"It is a great success that the Lebanese army has achieved over the terrorists, those who sought chaos, destruction and tragedies for Lebanon."
Siniora repeated a promise to the thousands of Palestinian refugees who have fled the camp in the early days of the fighting to rebuild the devastated area.
But he said that the camp would be placed under the authority of the state and "only the Lebanese state".
At present, Palestinian camps in Lebanon are forbidden from being accessed by the Lebanese state under a decades-old Arab agreement.
Khodr said Siniora's statement that the Nahr al-Bared camp will be under Lebanese security contrasted with the usual control of refugee camps by various Palestinian factions.
"Maybe what Siniora meant [in his statement] is that if the Lebanese authorities will take control of Nahr al-Bared it could be the first step in the Lebanese authorities taking control of other camps," she said.
Palestinian factions had yet to react to Siniora's statement.
Lebanese army forces continued their search on Monday for Fatah al-Islam fighters who may have succeeded in fleeing Nahr al-Bared on Sunday.
According to the army, Fatah al-Islam fighters attacked their positions while trying to escape the encircled camp early on Sunday.
A senior security source said: "Most of the terrorists were killed today, the others have been captured. A few might have escaped, but the army is hunting them down."
|Lebanese soldiers killed at least 40 Fatah|
al-Islam fighters in the final battle [AFP]