"Our forces are 400 metres (yards) from Al-Mishleb", a neighbourhood in the eastern outskirts of Raqa city, said Syrian Elite Forces spokesman Mohammad Khaled Shaker.
Rami Abdel Rahman, head of the Syrian Observatory for Human Rights monitor, said the advance came after heavy air strikes from the US-led coalition fighting IS.
The coalition has been backing a Kurdish-Arab alliance, the Syrian Democratic Forces, which in November launched an offensive to capture Raqa city from the jihadists.
The SDF have approached Raqa from the north and the west, but are still far from launching an assault on the city.
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The alliance is only three kilometres (almost two miles) from IS's de facto Syrian capital to the north, but as far as 25 kilometres from it to the west.
The jihadists still control areas south of the city.
The SDF was created in 2015, after IS overran large parts of Syria and neighbouring Iraq in 2014.
They joined the anti-IS offensive in December 2016.
The battalion is headed by Ahmad Jarba, who led top Syrian opposition body the National Coalition from July 2013 for a year.
Syria's conflict has killed 320,000 people since it started in 2011 with anti-government protests. It has since evolved into a complex war involving jihadists and world powers.