The Free Syrian Army has withdrawn all its main fighting units from its stronghold in the war-ravaged suburb of Salahedin in southern Aleppo.

The withdrawal was ordered just after sunrise on Thursday after a night of intensive shelling from planes and tanks on all three rebel frontlines. Commanders in Aleppo claimed the pullout was tactical and said a small force had remained behind to oppose any advance by regime forces.

However, the rebel move seems to mark a significant moment in the fight for control of southern Aleppo – which has raged for more than two weeks, claiming several hundred casualties, and laid the rest of the city to siege.

Shelling intensified on Thursday in other parts of Syria's second city, which had notionally been held by the FSA since it secured its foothold in Salahedin in late July.

The regime push had been widely expected earlier this week and rebels had vowed to defend their ground. However, commanders said the intensity of the shelling had meant their fighters now had too few opportunities to take cover.

"They were shelling the buildings at the frontline all night," said Major Abu Furad, who led one of the main units in Salahedin, Katiba al-Ansar. "The buildings were falling in front of us. It was impossible to stay there."

The rebel group had been occupying an area known as street 15, which faced a regime force around 200 metres away. Both sides had traded small arms fire for the past fortnight, but neither had advanced beyond their positions.

"We withdrew to street 10, which [runs parallel] behind street 15, 150 metres back," he said.

"But the regime was shelling that street too. It was relentless and no one could stay behind.

"They have started using bigger bombs from planes. They were far bigger than the shells from the tanks."

The FSA leadership in Aleppo says it is now redeploying its forces to other key areas of the city. It claims its ousting from Salahedin has not damaged morale and maintains that the regime is continuing to hold back its ground forces because it fears many would defect if they were ordered to enter the city.

"That's what the defectors are telling us," said Sheikh Tawfik Abu Sleiman, the leader of one of the Aleppo brigades. "They would shed their uniforms and run away."

Shelling intensified throughout Thursday in other areas of Aleppo that had so far seen limited fighting. The FSA said it was responding by launching attacks in the centre of the city, where regime troops and the loyalist shabiha militia were stationed to defend key state institutions.

The FSA in Aleppo seemed to be united in a plea for an internationally enforced no-fly zone, which would ground the Syrian air force jets now playing an increasing role in the campaign.

"That's all we need," said Abu Hanefa. "No guns, no armies, just the ability to get these things out of the sky. They are killing us."

Another rebel leader, who had left Salahedin, said: "Even the bravest among us had to acknowledge that these jets are something that we cannot fight. It is one thing being outgunned by tanks, but planes are creating a very, very difficult situation."