The Yarmouk camp has been the scene of heavy clashes in the past, but the battles subsided last month after Syrian rebels fighting to topple Syrian President Bashar Assad, battled loyalists there to a standstill.
In Tuesday's fighting, five people were killed on Yarmouk Street, four of them when a shell exploded and the fifth in sniper fire, according to The Britain-based Observatory for Human Rights that relies on reports from activists on the ground.
The group said intense clashes were taking place on the edges of the camp, where the Syrian troops are positioned, and the nearby Hajar Aswad district.
In a statement on Tuesday, representatives of 14 Damascus-based Palestinian factions called for a cease-fire and a halt to all military operations to enable medical teams and food supply trucks to enter the camp. They urged gunmen to withdraw from the camp "in order not to bear the responsibility of the continuing displacement of (Yarmouk's) residents."
About half of Yarmouk's 150,000 residents have fled since fighting erupted in mid-December, according to estimates by the United Nations Relief and Works Agency for Palestine Refugees that administers Palestinian camps in the Middle East. Some sought refuge in neighboring Lebanon, and others found shelter in UNRWA schools in Damascus and other Syrian cities.
Dozens have been killed in the fighting, although the United Nations did not provide an exact figure of casualties in Yarmouk violence that has included airstrikes and artillery shelling from the Syrian military and clashes between rebels and Assad loyalists.
Khaled Abdul-Majid, a senior representative of the Palestinian factions that issued the statement, confirmed that battles were progress in and around Yarmouk. He told reporters in Damascus, "We are working to end those clashes."
When the revolt against Assad's rule began in March 2011, the half-million-strong Palestinian community in Syria stayed on the sidelines. As the civil war deepened, most Palestinians backed the rebels, while some groups - such as the Popular Front for the Liberation of Palestine-General Command - have been fighting alongside the troops. The PFLP-GC joined the call for a truce on Tuesday. The group is led by Ahmed Jibril, a long-time Assad ally.
Yarmouk is the largest of nine Palestinian camps in Syria. Since the camp's creation in 1957, it has evolved into a densely populated residential district just five miles (eight kilometers) from the center of Damascus. Several generations of Palestinian refugees live there, some employed as doctors, engineers and civil servants and others as day laborers and street vendors. Many Syrians have also moved into the camp area over the years.
Elsewhere in the country, The Observatory and other activists reported heavy fighting on Tuesday in the suburbs of Damascus, including the Sayda Zeinab district, and reported shelling of the towns of Beit Saham and Aqraba, both near Damascus airport.
The Observatory also said three shells were fired at the suburb of Jaramana, wounding nine people.