However, the advance toward the central city from the west, reported by a pro-government newspaper and a monitoring group, and stepped up air strikes, do not indicate an imminent offensive to retake it.
IS overran Palmyra on May 21, sparking fears that the radical Sunni Muslim group might repeat the sort of vandalism it has carried out in Iraq and destroy one of Syria's most famous archaeological sites.
"The infantry has made tangible progress in the area of Biyarat al-Gharbiyeh," west of Palmyra, which had previously been in IS hands, said Al-Watan newspaper.
The Britain-based Syrian Observatory for Human Rights, which has been monitoring the conflict, said the army was now 10 kilometres (six miles) away from Palmyra.
More From This Section
The monitor, which relies on a network of sources on the ground, said that President Bashar al-Assad's troops had "chased IS fighters from Biyarat al-Gharbiyeh on the weekend".
Observatory head Rami Abdel Rahman said the capture of the area "allows the regime to secure a transport route for oil from the Jazal field... To other Syrian cities under its control."
Abdel Rahman said the government depends on gas and oil fields around Palmyra to provide electricity to cities under its control, namely Damascus.
He said the army's advances are just to protect these fields and that he doubted that an offensive on Palmyra was imminent, noting that the government has no popular support in the city.
The army's reinforcements to Biyarat al-Gharbiyeh came as Palmyra's new city was hit by heavy regime raids in the past few days that killed 11 people, said the Observatory.