The army's advance towards the Castello Road, brought it to within its firing range, came during a 72-hour past hours.
Rebels said they were fighting to retake lost positions and re-secure the road.
Its capture brings the Syrian government closer to its long-standing objective of encircling rebel-held areas of the northern city.
Aleppo, which was Syria's largest city before the civil war with a population of more than 2 million people, has been divided for years into rebel and government sectors.
Heavy aerial and artillery bombardment had at times made the Castello Road impassable.
But latest advance brings government forces the closest so far to the road, making it even easier to hit and effectively cutting off the opposition-held sector of the city near the Turkish border.
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