The Syrian army said it has recaptured the ancient city of Palmyra from ISIL for the second time in a year with help from allied forces and Russian warplanes.

The Islamic State of Iraq and the Levant group seized Palmyra in a surprise advance in December after having been driven out eight months before.

"With backing from the Syrian and Russian air forces, units of our armed forces recaptured the city of Palmyra, in cooperation with the allies," the military said in a statement.

The army and Iranian-backed militia advanced inside Palmyra on Thursday as ISIL withdrew completely, the Syrian Observatory for Human Rights, a Britain-based war monitor, said.

ISIL retreated to areas in the east, the Syrian Observatory reported. Government forces took control of swathes of Palmyra and conducted combing operations to clear land mines, it said.

During ISIL's first occupation, which ended in March last year, the armed group destroyed some of Palmyra's priceless archaeological heritage. It is believed to have razed other parts of the historical ruins after regaining control in December.

The Syrian army is also fighting ISIL east of Aleppo city, where it is pushing to reach the Euphrates River, and in the city of Deir al-Zor, where it controls an enclave besieged by fighters.

ISIL is on the back foot in Syria after losing territory in the north to an alliance of US-backed Kurdish-led militias, and to Turkey-backed Syrian rebel groups.

Government and opposition delegations are attending UN-sponsored peace talks in Geneva, where the government's chief negotiator hailed Syrian President Bashar al-Assad for keeping his promise to retake Palmyra.

The Syrian opposition, however, declined to congratulate Assad on capturing Palmyra and suggested the city changing hands again was possible.