The Syrian military was closing in on a Palestinian refugee camp outside Damascus on Tuesday, opposition activists said, following two days of shelling, dpa reported.
The reinforcements were brought in overnight to the outskirts of the al-Yarmouk camp, after fighters from the rebel Free Syrian Army said they were controlling most areas inside the camp.
The move has prompted an exodus from the camp to safer areas in Damascus and neighbouring Lebanon.
"About 2,000 Palestinian refugees from Syria crossed to Lebanon in buses and cars (since late Monday)," a Lebanese border official told dpa.
Al-Yarmouk is the largest Palestinian refugee camp in Syria, with 150,000 inhabitants.
Some of those who arrived in Lebanon said the Syrian government has given the refugees until Tuesday to leave the camp, raising fears of an imminent attack, according to opposition activists.
In Washington, State Department spokeswoman Victoria Nuland said Monday that the attacks on al-Yarmouk showed there has been no change in "the regime's behaviour, including the brutality it's inflicting on its own people."
Syrian Foreign Minister Walid al-Moallem, in a letter addressed to UN Secretary General Ban Ki-moon, insisted that the "Palestinians must not harbour terrorist groups inside the al-Yarmouk camp."