“Around 400 families, approximately 2,000 people, were able to leave the camp on Friday and Saturday via two secure roads to the Zahira district, which is under army control,” said Anwar Abdul Hadi, a Palestine Liberation Organisation official.
Abdul Hadi said Syrian troops had helped in the evacuation, which came as Palestinian forces battled to hold back IS fighters who have captured large swathes of the camp since Wednesday.
He said most of those evacuated from the camp were being hosted in government shelters, with at least 25 wounded taken to two hospitals in Damascus.
The Syrian Observatory for Human Rights, a Britain-based monitoring group, confirmed that “hundreds” of people had been evacuated from the camp.
The group said at least 26 people, including civilians as well as fighters from IS and Palestinian factions, had been killed in the camp since Wednesday.
Since the militant advance, regime forces have pounded the camp with shells and barrel bombs, according to the Observatory.
Palestinian officials and the UN agency for Palestinian refugees UNRWA have urged humanitarian access to the camp.
Yarmouk, in south Damascus, was once home to 160,000 people, Syrians as well as Palestinians.
But its population has dwindled to just 18,000 since the uprising erupted in March 2011.
The camp is encircled by government forces and was under a tight siege for more than a year.
An agreement last year between rebels and the government, backed by Palestinian factions, led to an easing of the siege, but humanitarian access has remained limited.
IS fighters attacked the camp on Wednesday, and were initially largely repelled, but were subsequently able to capture large parts of it.
Palestinian officials have accused Al-Qaeda’s Syrian affiliate Al-Nusra Front of helping IS to enter the camp.
Among the deaths in the fighting were at least two Palestinian militants reportedly beheaded by IS, according to the Observatory and extremist social media accounts.
Syrian forces remain outside the camp, and sources said troops had set up additional checkpoints around Yarmouk after the fighting began.