The Syrian government sent thousands of reinforcements to mount a counterattack Monday in Aleppo after rebels broke through government lines two days earlier, a monitoring group said.

Meanwhile, triumphant rebels vowed that a "new stage" in their offensive would aim to "liberate all of Aleppo," after they fought their way through Saturday to the besieged opposition-held eastern sector of the city.

The Lebanese Shiite Hezbollah movement and the Syrian government have mobilized more than 3,000 troops and militia fighters for an attempt to recapture the areas where the rebels made their breakthrough, according to the Syrian Observatory for Human Rights.

"Hundreds of opposition fighters have also arrived in Aleppo from the [neighbouring] province of Idlib to help in the expected battles," said Rami Abdel Rahman, head of the Britain-based monitoring group.

Hezbollah's battle-hardened fighters have provided crucial support to Syrian President Bashar al-Assad's overstretched army.

Syrian state news agency SANA said government planes carried out "intensive strikes" on "terrorist movements" south of Aleppo.

The regime acted to dismiss fears that the rebel advances would cut supply lines to government-held western Aleppo.

SANA quoted provincial Governor Mohammed Marwan al-Oulabi as saying that all essential goods and fuel were available in the area.

"Dozens of fuel tanks entered Aleppo city on Monday," he said.

Abdel Rahman confirmed that trucks loaded with fuel and food supplies had been able to reach western Aleppo through the north-western Castello Road area, which the regime captured from the rebels in July, severing what was then the last supply route into the east.

The opposition, however, appears so far to have been unable to secure supplies into the east, with heavy airstrikes continuing around the Ramousseh area where the rebels made their breakthrough.

Syria's largest city before the war, Aleppo has been divided between government forces in the west and rebels in the east since fighting erupted for control of the city in mid-2012.

The rebels claimed to have broken a four-week siege imposed by the regime on the opposition-controlled neighbourhoods in eastern Aleppo, a claim denied by Damascus.

There are thought to be about 250,000 to 300,000 civilians resident in the east, and about 1.2 million people in the western sector.

The situation in Aleppo is "extremely fluid," US State Department spokeswoman Elizabeth Trudeau said Monday, urging all parties to allow delivery of humanitarian aid to all residents of Aleppo.

"We are very focused on the impact on civilians right now," she said.

US-backed, Kurdish-led forces said Monday that they had captured 90 per cent of the strategic city of Minbij, north-east of Aleppo, from Islamic State.

The Minbij Military Council said that it would allow all Islamic State militants to leave the city in exchange for the release of civilians, accusing the group of using them as human shields.

Capturing Minbij and its hinterland would cut off Islamic State from its last access route to the border and the outside world.

The international medical charity Doctors Without Borders (MSF) said a busy hospital in a rebel-held area of north-western Syria was destroyed in airstrikes Saturday, killing 13 people.

Four staff at the hospital in Milis, west of Aleppo, and five children were among the victims, MSF said Monday, noting that the hospital, which the group supported, served a population of 70,000.

MSF did not attribute blame for the strike. Rights groups and analysts have previously accused Russia and the Syrian government of deliberately targeting hospitals in rebel-held areas.

In May, the UN Security Council passed a resolution demanding protection of hospitals in conflict zones, days after at least 30 people were killed in an airstrike on a hospital in eastern Aleppo.

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