Speaking by phone to U.N Secretary-General Ban Ki-moon on Monday, Syrian Foreign Minister Walid Al-Moallem warned the Palestinian refugees against helping the rebels.
He "stressed the need for the Palestinians to refrain from supporting or harboring these armed group which are intruders to the camp and help expel them," according to Syrian state news agency SANA.
UNRWA, the U.N. agency for the Palestinian refugees, said that "credible reports point to civilian deaths, injuries and destruction of property in Yarmouk."
Thousands are fleeing the camp in search of safety, the agency said. UNRWA is now housing more than 2,600 displaced people in the Damascus area, a number that is rising fast, it said. Initial reports suggest well over 2,000 Palestinian refugees have also sought refuge in Lebanon, it said.
The agency "remains gravely concerned about the safety of the Palestine refugee population in Syria and appeals to all parties to refrain from actions that endanger civilian lives and property," it said.
U.N. humanitarian chief Valerie Amos said via Twitter that she was horrified by the bombing of the camp. "Senseless loss of life. Civilians must not be targeted," she said.
U.S. State Department spokeswoman Victoria Nuland said the latest attacks "mark a significant and alarming escalation of the conflict in Syria. All parties must stop unlawful attacks on civilians and comply with international law."
Palestinian Authority President Mahmoud Abbas has urged combatants in Syria "to spare our camps and our people in Syria" and not draw the Palestinians into the civil war. He also called on the world community "to take immediate action" to protect Palestinians in Syria.
Rebels and the government have gained and sought support from Palestinians in Syria.
Many displaced Palestinians have been living for decades in Yarmouk, a nearly square-mile district inside Damascus about five miles from the center of the city.
Formed in 1957, the urban enclave is the largest Palestinian refugee community in Syria, with more than 148,500 registered refugees, the United Nations said.
At least 28 people have been killed across Syria on Tuesday, including nine in Damascus, according the LCC. Two children are among the dead, the activist network said.