Battered by days of fighting between Islamic militants and the Lebanese army, a steady stream of Palestinians has fled a refugee camp near Tripoli, Palestinian and Red Crescent officials said.

Fighting between the Fatah el-Islam group and Lebanese troops had died down by Wednesday morning, allowing about 2,000 Palestinians to seek shelter in alternative camps or emergency accommodation, the Red Crescent said.

Deadly clashes at the Palestinian camp began Sunday when Lebanese Internal Security Forces raided a building in a neighborhood north of Tripoli, army sources said.

Militants from Fatah al-Islam began shooting at the forces, who returned fire, triggering fighting in the vicinity of the camp.

Video from the camp on Tuesday showed some leaving on foot, carrying babies and a few belongings, and others crowded into cars and vans.

Many of those leaving carried makeshift white flags or waved them from car windows. An elderly woman wept as she sat in a wheelchair waiting to be taken from the camp.

The Red Crescent said it had helped the refugees get to another camp at Beddawi, about seven miles away. Red Crescent officials said snipers had fired at some refugees as they left the camp.

According to Aslan, militants were hard to find at the refugee camp on Wednesday.

"As far as I know there are very few fighters from Fatah el-Islam left in the camp -- some are leaving the camp I heard," Aslan said. "But we don't know that much about them because we don't have any relationship with them."

It's not clear how many civilians were killed or injured during the fighting at the Nahr el-Bared camp. At one hospital nearby, Dr Ahmad El Kheir told CNN he expected dozens more casualties from the camp. (Watch an explanation of what's behind the fighting )

Earlier Tuesday, a U.N. convoy trying to deliver relief supplies to the beleaguered camp was caught in crossfire. A U.N. official in Beirut said several of the agency's workers were trapped inside the camp for several hours, but later got out shaken but unhurt. It's not clear who fired on the convoy or whether it was targeted.

The convoy had entered the camp soon after Fatah el-Islam had declared a unilateral cease-fire beginning at 1130 GMT (7:30 a.m. ET). The Lebanese army had said it would not fire unless fired upon.

A spokeswoman for the U.N. Relief and Works Agency, Hoda Samara, told CNN from Beirut that the relief convoy had been loaded with water, food and medical supplies.

"The humanitarian situation is very, very bad," she told CNN, "and deteriorating every minute. Inside the camp there are no hospitals and only one health center," which had been unable to stay open during the fighting. The overcrowded camp was home to some 31,000 people.

In a separate incident, Lebanese security forces said they located a militant of Fatah el-Islam in a 10-story apartment block in Tripoli. After a six-hour stand-off, the militant blew himself up, according to the security forces.

Militant 'breeding ground'
Nahr al-Bared is about nine miles (16 kilometers) north of Tripoli, Lebanon's second-largest city that is home to a large population of Sunni Muslims.

The camp houses 31,023 registered refugees, according to the U.N. Relief and Works Agency. It is one of 12 Palestinian camps in Lebanon in which the United Nations operates. The agency estimates there are 350,000 refugees in the camps. (Facts on refugee camps)

The living conditions at the camp are partly to blame for the rise of Fatah al-Islam, according to Khalil Makkawi, a former ambassador to the United Nations. (Full story)

It is unclear whether the militant group has ties to al Qaeda.

Though Syria has claimed Fatah al-Islam is connected to the terror group, Lebanese Interior Minister Hasan al-Sabaa has described Fatah al-Islam as "part of the Syrian intelligence-security apparatus," according to Jane's Information Group, which provides analysis on international security matters.

Lebanon's economy minister on Monday asked for money and resources to help Lebanese forces battling the militants.

Assassination tribunal
The U.N. Security Council is considering passing a resolution that would enforce the establishment of an international tribunal to try suspects for the 2005 assassination of former Lebanese Prime Minister Rafiq Hariri.

That is an idea unpopular with the Lebanese militant group Hezbollah, which has links to Syria. Many people believe Syria was behind the killing.

The White House on Tuesday repeated its warning to Syria not to interfere in Lebanon in an effort to delay the international tribunal. In addition, the United States is planning to step up its assistance to the Lebanese army.

Military and diplomatic sources told CNN that the Lebanese government Tuesday sent Washington a request for more military assistance -- describing its most urgent needs as ammunition, helmets and armored vests.

Such supplies are allowed under a program the United States began last year to beef up the Lebanese army's capabilities, after Israel's war with Hezbollah. The program is worth about $40 million, and has mainly included basic items such as humvees, trucks and spare parts for helicopters.

Military officials say that the aim of such aid is to ensure that Lebanon does not become a haven for groups linked to al Qaeda.