Lebanese troops have reportedly come under attack from Islamist militants barricaded inside a Palestinian refugee camp in the north of the country.
A UN official says most families have now left the camp
Army posts were shelled and gunfire was heard late on Sunday, local TV said, despite an uneasy ceasefire deal.
Earlier, the head of the Fatah al-Islam group said his men would not surrender, despite a call by a key Druze leader for an end to the stand-off.
In Beirut, a grenade was thrown onto a road junction, injuring four people.
Two policemen and two civilians were hurt by the grenade, which was thrown in a mainly Sunni Muslim area of the city.
Call for justice
The latest violence around the Nahr al-Bared refugee camp flared as negotiations were said to be continuing with the Islamists of Fatah al-Islam.
Talks began hours after their leader, Shaker al-Abssi, said in a video message that Fatah al-Islam would "fight Jews, Americans and their allies".
Split from Palestinian group Fatah al-Intifada in late 2006
Believed to have 150-200 armed men, based in Nahr al-Bared camp
Denies al-Qaeda links but says it endorses its ideas
Has links with Syrian intelligence, Lebanon says
Leader is Shaker al-Abssi
Druze leader Walid Jumblatt, a supporter of Lebanon's governing coalition, said there were "no proposals" for a military solution.
"But we want the murderers handed over to Lebanese justice," he said.
A week of clashes at the camp has left dozens dead, including civilians, although a UN official said that about 25,000 had now fled the camp.
But Nahr al-Bared houses around 31,000 people and some people remain trapped inside.
The Lebanese army is still surrounding the camp and more reinforcements have been sent up.
A government official told the French news agency AFP that Lebanon has given Palestinian factions until the middle of the week to negotiate a peaceful end to the fighting.
On Saturday, Lebanese Prime Minister Fouad Siniora told the BBC that the militants would be treated fairly if they surrendered. If not, the authorities would "let the army deal with this matter", he said.
But in a video message released late on Saturday, the Fatah al-Islam leader ruled out surrender.
"O advocates of the US plan, we tell you that Sunnis will be a spearhead in fighting the Jews, Americans and their allies," he said.
The BBC's Kim Ghattas in Beirut says that Fatah al-Islam's leaders have now openly adopted the same discourse as al-Qaeda.
The group had previously said it was defending Muslims and Palestinians in Lebanon.
But other Palestinian groups have distanced themselves from Fatah al-Islam, which emerged last year after splitting from a Syrian-backed Palestinian splinter group.