BEIRUT, Lebanon — Syria warned its Palestinian refugee population on Monday not to aid the insurgency that is fighting President Bashar al-Assad, as hundreds of Palestinians fled the Yarmouk neighborhood of Damascus. Many headed for relative safety in Lebanon, a day after Syrian forces attacked that neighborhood with airstrikes for the first time in the civil war.

The Syrian warning appeared to reflect the importance that Mr. Assad attaches to the loyalty of the country’s Palestinians, an important element of what remains of his political legitimacy. It came as new clashes were reported in and around the Yarmouk neighborhood between government forces and rebel fighters.

Hundreds of thousands of Palestinians live in Syria, displaced by the Arab-Israeli struggle. Historically, they have considered Mr. Assad a benefactor and an ally. Yarmouk was originally a refugee camp and has developed into a mixed Damascus neighborhood where many Palestinians live. But increasing numbers of them have been siding with the insurgents.

The warning aimed at these Palestinians was conveyed in a news dispatch by SANA, the official news agency, about a telephone conversation between the country’s foreign minister, Walid al-Moallem, and the United Nations secretary general, Ban Ki-moon, concerning the general situation in Syria and specifically the Yarmouk neighborhood.

Mr. Moallem was quoted as telling Mr. Ban that mayhem had been convulsing Yarmouk for days, caused by infiltrations from terrorist groups, the government’s blanket description for insurgents.

The SANA account said that Syrian ground forces had refrained from entering Yarmouk, but said nothing about the Syrian air and artillery attacks that first hit Yarmouk on Sunday, which were reported by witnesses, rebels and Palestinian defectors to the rebel side. By some accounts, as many as 20 people were killed and dozens hurt, and families could be seen hastily fleeing the area with packed bags.

Martin Nesirky, a spokesman for Mr. Ban at the United Nations, confirmed that the secretary general had spoken with the Syrian foreign minister to express concern “about the escalation of violence in recent days, and very specifically the incident yesterday in which a Palestinian refugee camp, Yarmouk, right near Damascus, came under attack.”

The United States also expressed concern. Victoria Nuland, a State Department spokeswoman, said the aerial bombardment of Yarmouk constituted “a significant and alarming escalation of the conflict in Syria.”

In the aftermath of the bombardment, Syrian government tanks and dozens of troops could be seen taking positions at the northern entrance to Yarmouk on Monday as hundreds of people fled on foot, searching for taxis or buses to take them to safety in Lebanon and elsewhere. Some residents headed to schools where classes were abruptly stopped so that the buildings could accommodate fleeing families. Luckier refugees went to relatives living outside the neighborhood.

During a predawn announcement, Yarmouk mosques told residents to take advantage of a brief window of time, from 6 to 8 a.m., to flee the area, according to Yussef, a 40-year-old Palestinian refugee who hurried out of the camp with his family, carrying a large black bag in one hand and his 6-month-old baby in the other. “I couldn’t sleep the whole night,” he said. “I heard a lot of shooting, but I don’t know from where.”

He said he was shocked on Sunday at the speed of the government assault, in which fighter planes and artillery were used to attack the area hours after rebel fighters entered Yarmouk. One fighter said that the rebel goal was not to control the neighborhood but to use it “to move forward to the Damascus downtown and finish the regime.”

On Monday, groups of rebel fighters patrolled Yarmouk’s main street as the government forces shelled parts of the neighborhood. Yussef said he was moving his family to his brother’s house outside the camp.

“I want to save my family’s life,” he said. “I will never, ever return.”

In neighboring Lebanon, the minister of social affairs, Wael Abu Faour, said on Monday that at least 22 busloads of people had entered the country from Syria in the last day, and a “majority were Palestinians fleeing Yarmouk.”

More refugees were arriving on Monday at the border town of Masnaa, where entry lanes were clogged with Palestinians.

In another sign of Syria’s growing anarchy, the Italian Foreign Ministry confirmed Monday that three Europeans had been abducted by militants in Syria, identifying one of the three as Mario Belluomo, 63, an Italian citizen. Later, a spokesman for the Russian Embassy in Damascus confirmed that the other two hostages were Russian citizens, and that all three had been abducted around Latakia, a coastal city.