Sources close to government forces denied that they had been pushed aside and said they had driven the rebels back from an artillery base.
UK-based opposition activists say the rebels have indeed managed to link up with their comrades in eastern Aleppo.
But the rebels have so far failed to establish a secure route, they add.
The rebel coalition includes an al-Qaeda affiliated group.
Government forces cut Aleppo’s rebel-held areas off in July, with some 250,000 people living under siege.
Rami Abdel Rahman, head of the Syrian Observatory for Human Rights, a UK-based opposition news service, said the rebels had broken the siege but the route was “not fully secure yet”.
On Friday, the rebel groups said they had stormed an artillery base in the city.
But the Syrian army said it had repelled the assault and inflicted heavy casualties on the rebels.
Meanwhile, a US-backed alliance of Kurdish and Arab fighters seized most of Manbij – a key Syrian city – from so-called Islamic State.
Fawaz Gerges, who is professor of Middle Eastern Politics at the London School of Economics, told the BBC News Channel that the rebels had certainly made gains.
“The rebels coalition – it’s called the Army of Conquest – has basically made some major progress,” he said.