According to the UK-based Syrian Observatory for Human Rights, Syrian government troops were now only 1.2 miles south of the UNESCO World Heritage-listed ruins.
ISIS militants seized Palmyra and the adjoining modern town in May 2015.
They subsequently destroyed two 2,000-year-old temples, an arch and funerary towers, drawing global outrage.
ISIS, which has also demolished several world-renowned pre-Islamic sites in neighboring Iraq, believes that such structures are idolatrous.
UNESCO has condemned the destruction as a war crime.
The Syrian Observatory, which relies on a network of sources on the ground in Syria, told the AFP news agency that government forces were on March 23 only 1.2 miles from Palmyra’s southern outskirts and 3 miles from its western edge.
The governor of Homs province, Talal Barazi, confirmed the advance and said troops were now stationed on several hills overlooking the Greco-Roman ruins.
“There is continuous progress by the army from all directions,” he was quoted as saying by the Associated Press.
Talal Barazi added that he expected “positive results” over the next few days.
Syrian government forces launched an offensive to retake Palmyra at the beginning of March, backed by heavy Russian air strikes.
Last week, the Russian military said its aircraft were flying up to 25 sorties a day over Palmyra to help liberate what President Vladimir Putin has described as a “pearl of world civilization”.
Palmyra is also situated in a strategically important area on the road between Damascus and the contested eastern city of Deir al-Zour.
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