Short of food, water and electricity, the camp has been abandoned by most of its 40,000 residents.
At least 118 people, including 50 soldiers and 38 fighters, have been killed since the fighting began, making it Lebanon's worst internal violence since the civil war from 1975-1990.
The fighting began on May 20 when Fatah al-Islam fighters attacked army units deployed around Nahr al-Bared after one of their hideouts in a nearby city was stormed.
The latest mediation efforts by Lebanese parties to try to convince the fighters to surrender have had no success.
But Lebanese sources said the Islamic Action Front, which includes Sunni politicians and clerics, and a grouping of Palestinian clerics, would continue efforts to find a solution.
New army tactic
The Lebanese army command told Al Jazeera that Saturday's intensive shelling is aimed at tightening its grip around posts and hideouts of Fatah al-Islam.
The shelling now targets the centre of Nahr al-Bared refugee camp, whereas it previously target northeast areas of the camp, army sources said.
Hashem Ahelbarra, Al Jazeera's correspondent in Tripoli, said the military was targeting Sami district, thought to be the main stronghold of Fatah al-Islam.
"The Palestinian refugees are not being treated properly by Lebanon"
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He said: "The army is trying to send a strong message to the fighters of Fatah al-Islam that they will not tolerate what happened 22 days ago and that the only solution is to get rid of Fatah al-Islam fighters or at least, to have the senior leaders brought to justice."
The Lebanese army on Saturday also cut off the international road linking Tripoli city to the northern borders with Syria.
But a defiant Abu Hureira, Fatah Islam's deputy commander, speaking to The Associated Press by telephone from inside the camp, said: "We are steadfast and, God willing, we will not retreat for one moment.
"Let them [army] advance if they want ... We are on the front lines across from them."
Country in turmoil
Lebanon is already struggling with a seven-month-old political crisis, and there are fears that fighting could spread.
The past week has seen deadly clashes at another refugee camp and five bomb blasts in civilian areas in and near Beirut.
Fouad Siniora, the Lebanese prime minister, told the French television station TV5 on Friday that the army was holding back to preserve civilian lives.
"That's why this battle is taking longer, and it's worth pointing out that these terrorists are well-equipped and well-trained and persistent."
Authorities have charged 32 detained members of Fatah al-Islam with terrorism, charges that carry the death penalty.
Source: Al Jazeera and agencies