"The regime forces are now two kilometres (a little more than a mile) away on the south side and five kilometres away on the west side," Syrian Observatory for Human Rights director Rami Abdel Rahman told AFP.
IS seized the city dubbed the "Pearl of the Desert" in May last year, sending shock waves around the world as the group demolished some of the most treasured monuments of its UNESCO-listed World Heritage Site.
IS has fiercely resisted the advance, killing at least 26 pro-government fighters on Monday alone, the Observatory said.
Aamaq, an IS-linked website, claimed that 30 troops were killed in an attack by a jihadist suicide bomber.
The recapture of Palmyra would be a strategic as well as symbolic prize for the regime.
Whoever controls the oasis city also controls the surrounding desert -- an area of some 30,000 square kilometres extending to the Iraqi border.
That would cut IS's area of control from some 40 percent of Syrian territory to 30 percent, according to the Observatory.
The jihadists have waged a sustained campaign of destruction against heritage sites in areas IS controls in Syria and Iraq and in mid-August last year beheaded Palmyra's 82-year-old former antiquities chief.
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