"The army has entered a western neighbourhood of Palmyra and has seized control of part of it," Rami Abdel Rahman, head of the Syrian Observatory for Human Rights, told AFP.
"There are clashes and heavy shelling" across the historic city, said the monitoring group's chief.
Abdel Rahman said earlier that Syrian forces, backed by Russian soldiers, had captured a string of hilltops overlooking Palmyra, bringing them within firing range of its western half.
"They are close to capturing the citadel. IS withdrew from it, but they may have left suicide bombers inside," he said.
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IS jihadists first seized Palmyra in May 2015 and began to systematically destroy the city's monuments and temples, while also looting its many archeological treasures.
They were driven out in March 2016 but recaptured the town last December.
Syrian state media confirmed today that government forces were now in control of key territory around Palmyra.
"Seizing control of Mount Hilal and other hilltops overlooking Palmyra is an important step towards the collapse of the terrorist groups in the city," state news agency SANA said.
"This crossroads is the key to entering the city," the source told AFP.
IS has ravaged the city's celebrated heritage, blowing up funerary towers and carrying out mass executions in the city's Roman theatre.
Last month, IS destroyed Palmyra's tetrapylon monument, while satellite images showed damage to the theatre's facade.
The new destruction was condemned by the United Nations as a "war crime."
Today, two funeral busts damaged by IS after it first captured Palmyra were brought back to Syria after being restored in Italy.