BEIRUT (Reuters) - Islamic State in Iraq and Syria (ISIS) militants have withdrawn from areas in the historic city of Palmyra they had seized on Saturday, a group monitoring the conflict in Syria and a Syrian official said.

The militant group's attack on the government-held city of Palmyra, also known as Tadmur, has raised concern its World Heritage site could meet the same fate as ancient monuments the group has destroyed in Iraq.

The Syrian Observatory for Human Rights, a British-based monitoring organisation, said ISIS fighters had pulled out of northern areas of the city taken on Saturday but still held a village to the north of Palmyra.

Maamoun Abdulkarim, the Syrian government's antiquities chief, told Reuters the army had regained control of the whole city, and that the ancient ruins to the south-west of the city were unharmed.

"The outskirts they had entered were all recovered," he said.

Palmyra is strategically significant because it sits at a crossroads linking it to the cities of Homs and Damascus.

ISIS has mounted frequent attacks on government-held areas in recent months, part of an apparent effort to expand beyond its strongholds in eastern and northern Syria.

Syrian state TV, citing a military source, said the army had killed dozens of ISIS militants to the east of Palmyra and were "pursuing their withdrawing remnants in several directions in the area".