Without naming the Assad regime by name, he urged "all parties involved in the Syrian conflict to refrain from harming our people in the refugee camps. At least 25 people died in the Sunday attack.
"Don't drag them into your fighting," he said in Rome.
An online video purporting to be of the Yarmouk Camp on the southern edge of Damascus showed several bodies and body parts in the street and on the steps of the Sheik Abdul Qader mosque.
Opposition activists said the mosque had offered shelter to Palestinians and others displaced by fighting in other areas.
Minutes before, a Syrian jet fighter fired rockets at the camp, activists said of the 112,000-population mixed Syrian-Palestinian neighborhood at the heart of a struggle for the capital's southern suburbs.
For many Yarmouk Palestinians, the attacks ended the last vestiges of the Assad regime's claim to be a Palestinian champion and protector, the Times said.
"For decades the Assad regime was talking about the Palestinians' rights," a Palestinian refugee who gave his name as Abu Ammar told the Times. "But [Syrian President] Bashar Assad has killed more of us today than Israel did in its latest war on Gaza."
As the fighting raged, Syria's vice president called for a "historic settlement" and a national unity government after saying neither side could decisively win the 21-month-long hostilities that have devolved into civil war.
"The solution has to be Syrian, but through a historic settlement, which would include the main regional countries and the member of U.N. Security Council," Farouk al-Sharaa told the Lebanese newspaper al-Akhbar in an interview published Monday.
"This settlement must include stopping all shapes of violence, and the creation of a national unity government with wide powers," he said.
Al-Sharaa, who was Syria's foreign minister from 1984 until becoming vice president in early 2006, said neither the rebels nor the Assad regime had the military ability to reach "a conclusive end" to the war that has killed an estimated 40,000 people.
He said the fighting was now about the country's very existence, not "the survival of an individual or a regime," and said Syria's leaders "cannot achieve change without new partners."
Sharaa, the most-senior Sunni Muslim member of President Bashar Assad's minority Shiite Alawite-dominated regime, was reported by the opposition in August to have defected to Jordan, but he later resurfaced in Damascus.
Syrian rebels have said they are open in theory to al-Sharaa leading an interim government, CNN reported -- an idea proposed by Turkish Foreign Minister Ahmet Davutoglu in October and floated by the Arab League.
But The New York Times said many Assad opponents reject dealing with any current-regime leader.
"Every day that passes, we are moving further away from a military or political solution," al-Sharaa told the newspaper.
"The various opposition forces -- whether armed or civilian, or linked to foreign powers -- cannot claim they are the sole legitimate representatives of the Syrian people," he said.
"The current governing power, with its army possessing its own ideology, as well as its political parties, with the [Assad-led] Baath Party at the forefront, cannot alone create changes without new partners," he said.
Al-Sharaa's comments were his first published statements since July 2011.
Separately, Iran put forward a six-point plan to end the war Sunday, including a halt to arms shipments, the release of political prisoners and a broad-based dialogue to form a transitional government that would hold free elections, Iran's state news agency reported.