The latest battle erupted at dawn at the coastal Nahr al-Bared camp just outside the northern port of Tripoli, Lebanon's second largest city.
Medical sources inside the camp appealed for fighting to stop, saying there were dead and wounded lying on the streets.
Dark smoke rose from the camp as shells crashed among the densely-packed breeze-block buildings. ''We can hear very intense shelling, it's constant,'' said a Reuters witness.
At least 20 militants, 32 soldiers and 27 civilians have been killed since fighting between the army and Fatah al-Islam fighters erupted early on Sunday, making it Lebanon's worst internal violence since the 1975-1990 civil war.
Fifty-five soldiers have also been wounded.
Palestinians in the camp yesterday said thousands had fled homes on the edges of Nahr al-Bared, where fighting was most intense, to seek shelter deeper inside. More than 150 people had been wounded and dozens of homes destroyed, they said.
The renewed bombardment began hours afrer Prime Minister Fouad Siniora's government stressed the need to put an end to Fatah al-Islam, a Sunni Muslim group with al Qaeda sympathies.
The group emerged late last year and has little support across Lebanon's deeply divided political spectrum. It has only a few hundred fighters, but they are well-armed and motivated.
Based in Nahr al-Bared, the group is thought to have links with jihadist factions in other Palestinian camps.
''We are going to continue fighting until the last shot.
There will not be another Jenin massacre,'' Abu Salim, spokesman for Fatah al-Islam, told Reuters by telephone, referring to an Israeli assault on a refugee camp in the West Bank in 2002.
A Lebanese security source said the army had tightened its grip around the camp. ''There have been clashes and exchange of gunfire. The army is firing at any source that is firing on the army,'' the source said.
CHALLENGE TO ARMY The United States, which firmly backs the Beirut government, said Lebanon was justified in attacking the militants.
''Extremists that are trying to topple that young democracy need to be reined in,'' US President George W Bush said.
But Bush, though deeply distrustful of Syria's role in Lebanon, stopped short of accusing Damascus of involvement.
''I'll be guarded on making accusations until I get better information, but I will tell you there's no doubt that Syria was deeply involved in Lebanon. There's no question they're still involved in Lebanon,'' Bush told Reuters.
Syrian Foreign Minister Walid Moualem repeated his country opposed Fatah al-Islam and wanted to arrest its leaders. ''Our forces have been after them, even through Interpol,'' he said.
The violence has posed a sharp challenge to Lebanon's army, which has traditionally been kept out of internal conflicts, as well as to Siniora's Western-backed government, denounced as illegitimate by Syrian-backed and other opposition factions.
While eliminating Fatah al-Islam is an aim most Lebanese parties would support, any army attempt to storm Nahr al-Bared might result in heavy civilian casualties and would violate a longstanding Arab agreement which has kept Lebanon's 12 refugee camps off limits to Lebanese security forces since 1969.
While fighting rages in the north, Beirut has not escaped unscathed.
A bomb exploded in a shopping area in the mainly Sunni Muslim area of Verdun last night, wounding at least seven people, security sources said. It appeared to mirror an explosion on Sunday that killed a woman and wounded 10 people in a mainly Christian district of the capital.
(Additional reporting by Ali Ghamloush) REUTERS SM HS1241