Lebanese troops and Islamist militants have clashed in the city of Tripoli for a second day, after earlier violence left about 50 people dead.
On Sunday, Lebanese troops fought running battles with the militants
Troops shelled Fatah al-Islam positions around the Nahr al-Bared refugee camp, the focus of much of Sunday's fighting.
More than 20 soldiers and 20 militants were killed in Sunday's clashes, and an unconfirmed number of civilians.
It was Lebanon's bloodiest internal fighting since the country's civil war ended 17 years ago.
The information minister said troops would hunt down the Islamist group.
"There are security procedures under way," Ghazi Aridi said. "We had casualties, but we will continue and those cells have also suffered casualties."
Mr Aridi said the militants killed on Sunday included "key leaders who have carried out and have been planning to carry out large attacks".
One of the dead militants was wanted in Germany over an unsuccessful plot to blow up trains last July, Lebanese security officials told journalists.
The situation seems to have basically stabilised after the battles on Sunday, the BBC's Jim Muir reports from Beirut, with the Lebanese army regaining control of the camp's perimeter.
Split from Palestinian group Fatah al-Intifada in late 2006
Based in Nahr al-Bared camp, led by Shaker al-Abssi
Denies al-Qaeda links but says it endorses its ideas
Has links with Syrian intelligence, Lebanon says
Four members arrested over February bus bombings
But sporadic exchanges of fire continued during the night and in the morning the Lebanese army resumed pounding militant positions on the edge of Nahr al-Bared with tank and artillery fire.
Civilians are trapped inside the camp - home to around 30,000 displaced Palestinians - where conditions are worsening.
A handful of wounded have been taken out but it has been impossible to get outside help to many others, our correspondent adds.
Sunday's violence erupted after security forces raided a building in Tripoli to arrest suspects in a bank robbery.
Fatah al-Islam militants then attacked army posts at the entrances to the camp.
A large force of Lebanese troops hit back, bombarding the camp and storming a building on the outskirts of Tripoli.
A Lebanese civilian and a Palestinian refugee were also killed, the French news agency AFP said, and there were reports of a number of civilians killed inside the camp, Reuters news agency said.
More civilians were said to be wounded and a Lebanese army spokesman said another 27 soldiers were injured.
Later on Sunday, a woman was killed in a bomb blast near a shopping mall in Beirut's largely Christian eastern district of Ashrafieh. At least 10 people are said to have been hurt.
It is not clear if the blast was linked to the fighting in the north.
Lebanon is home to more than 350,000 Palestinian refugees, many of whom fled or were forced to leave their homes when Israel was created in 1948.
More Lebanese troops were brought in as the fighting developed
The Nahr al-Bared camp - which the military cannot enter under a 38-year-old deal - has been under scrutiny since two bus bombings in a Christian area of Beirut in February, blamed on al-Fatah Islam militants based in the camp.
Fatah al-Islam is a radical Palestinian splinter group alleged to have links with al-Qaeda. Lebanese officials also believe it has ties to Syrian intelligence.
Other Palestinian groups have distanced themselves from Fatah al-Islam, which emerged last year after splitting from a Syrian-backed Palestinian splinter group, our correspondent says.
Some link the eruption in violence to moves at the UN Security Council to set up an international tribunal to try suspects in the assassination of the former Prime Minister, Rafik Hariri, two years ago.
Syria is against the tribunal, and Lebanese government officials have accused Damascus of trying to stir up trouble to head it off.