The Lebanese army is shelling militant positions deep within the besieged Nahr al-Bared refugee camp, as its operation to force a surrender continues.
The fighting has intensified over recent days and nights
The army says militants from the Fatah al-Islam group have been cleared from the edges of the Palestinian camp during heavy fighting since Friday.
Prime Minister Fouad Siniora described the group as a "terrorist gang", and said there would be no negotiation.
A militant spokesman said they would fight to "the last drop of blood".
"We will not surrender," vowed Fatah al-Islam spokesman Abu Salim Taha.
"The Nahr al-Bared camp will not fall despite the destructive shelling, and the army will not be able to enter," he told the AFP news agency.
Fears for civilians
However, there were suggestions that the army was advancing and had forced militants into the southern part of the camp, after fierce battles on the northern and eastern edges, said the BBC's Kim Ghattas in Beirut.
But the reports could not be confirmed as the media were being kept at bay, she added.
The army has said its forces have not entered the camp itself, which is near Tripoli in northern Lebanon, since fighting broke out two weeks ago.
There is a longstanding convention that the army does not enter Lebanon's 12 Palestinian refugee camps, leaving security inside to militant groups.
More than 100 civilians, soldiers and militants are reported to have died in the two weeks of fighting.
There is great concern for civilians in the camp, who have no access to power or medical help, our correspondent says.
Tens of thousands are thought to have fled the camp since fighting broke out, but thousands reportedly remain.
Aid agencies have called for a ceasefire to allow more civilians to leave.
But the government and army are in no mood to end the siege now, our correspondent says.
Thousands of people have already fled the camp for shelter nearby
Prime Minister Fouad Siniora said the militants had to surrender.
If they did, he said, "they will face a fair trial", otherwise they would be crushed.
The violence is the worst internal fighting Lebanon has seen since the end of its civil war 17 years ago.
The fighting intensified on Friday, when Lebanese forces launched what some have described as the "final assault" on the camp.
On Saturday, troops pounded the camp with 155mm artillery fire, and used helicopter gunships overhead.
However, correspondents said the barrage on Sunday was less intense than in the last few days.