Lebanese tanks and armored vehicles battled their way into the outer neighborhoods of a Palestinian refugee camp Friday in some of the heaviest fighting since violence broke out between the military and al-Qaida-inspired militants nearly two weeks ago.

The military demanded the Fatah Islam fighters holed up in the Nahr el-Bared camp in northern Lebanon surrender and promised to pursue them if they didn't.

Two Lebanese soldiers were killed and 10 wounded in Friday's fighting, according to security officials who spoke on condition of anonymity because they were not authorized to address the media. They said a unit of Fatah Islam militants was destroyed, but gave no casualty count.

Friday's deaths raised to 34 the number of soldiers killed since fighting between the army and militants began on May 20. At least 20 civilians and about 60 militants also have been killed in the 13 days of fighting, but it was unclear whether there were any civilian casualties Friday.

Most of the camp's 31,000 refugees have fled, many to the nearby Beddawi refugee camp.

The army appeared to have limited Friday's advance to neighborhoods on the outer ring of the camp, which militants use for sniper fire against army positions. Nahr el-Bared, like the other 11 Palestinian camps in Lebanon, has been off-limits to Lebanese authorities under a nearly 40-year-old agreement that allowed Palestinians to run their own affairs.

The Palestinian representative to Lebanon, Abbas Zaki, said the army would not storm into the camp, where several thousand civilians remain trapped and militants are barricaded in residential neighborhoods of narrow, winding streets and apartment buildings.

A soldier at the scene said troops were fighting from building to building. A resident of the camp, speaking on condition of anonymity for fear of militant reprisals, said some Fatah Islam positions were overrun or destroyed.

The army later issued a statement saying it destroyed positions from which the militants attacked troops and civilians, and "tightened the ring" around them, causing many casualties. The statement said other militants had fled deeper inside the camp, taking civilians as "human shields."

"What we have decided is to deal with Fatah Islam as a group, a terrorist group taking hostages who are left in the camp," said Telecommunications Minister Marwan Hamadeh. He told AP Television News in Beirut that the army may be seeking to isolate the militants.

Cabinet Minister Ahmed Fatfat told Al-Arabiya television the army came under sniper fire early Friday and decided to respond. "It seems they have destroyed those positions."

The bombardment sent clouds of white smoke rising from the camp throughout the day, and the shelling ignited fires that spewed black smoke.

The fighting between the army and the Fatah Islam group erupted in the northern port city of Tripoli and the adjacent Nahr el-Bared camp on May 20. At least 22 soldiers and 17 militants were killed that day — the worst internal violence in Lebanon since the end of the 1975-90 civil war.

After three days of heavy clashes, the government agreed to a truce to give Palestinian mediators and Islamic clerics time to persuade the militants to surrender. Thousands of residents then fled the camp.

Several hundred militants inside Nahr el-Bared continued to target troops with sniper fire, however, vowing to fight to the death. Political support also has grown for the army to resolve the conflict through military action.

However, limiting the military operation to the camp's perimeter could be an effort to avoid — at least for now — enraging Palestinians in other refugee camps across the country.

Fatah Islam is an offshoot of the pro-Syrian Fatah Uprising, which broke from the mainstream Fatah movement in the early 1980s, Lebanese officials say.

Some Lebanese security officials consider Fatah Islam a radical Sunni Muslim group with ties to al-Qaida or at least al-Qaida-style militancy and doctrine. Others say it is a front for Syrian military intelligence aimed at destabilizing Lebanon.

Many Palestinian refugees support the army's moves against the militants, whom they consider alien to the camp's population. Zaki, the Palestinian representative, said after meeting with Prime Minister Fuad Saniora that he hoped the militants would "surrender to justice."

In the Beddawi camp, about 500 Palestinians demonstrated after Friday noon prayers, demanding an end to the fighting. A group of mothers staged a sit-in outside a school that has been turned into a refugee center and stopped trucks from delivering relief.

Mohammed Abu Hussein, 26, a computer technician from Nahr el-Bared who fled to Beddawi, said the militants were "so fanatical, they would rather die than surrender."

"So the army has no other choice but finish them off," the Palestinian said.