By Suleiman Al-Khalidi

BEIRUT (Reuters) - Syrian rebel fighters have launched a major assault on government-held southwestern parts of Aleppo to try to reopen supply lines into opposition-held areas of the city after the army and its allies tightened their siege last week.

The rebels are trying to break through a strip of government-controlled territory in the hope of reconnecting their area of control in the west of Syria with the encircled sector of eastern Aleppo.

A rebel military command centre that includes the newly formed Islamist group Jabhat Fatah al Sham, formerly the al Qaeda-linked Nusra Front, Ahrar al Sham and Free Syrian Army (FSA) brigades said they had seized army positions and some residential compounds in the first few hours of the assault, which began on Sunday night.

Later, rebels said they had captured the strategic al-Mishrefah area, south of the Ramousah air force artillery base, which has been used to pound rebel-held areas from its fortified hilltop position.

"There is fast and quick progress," said Abdul Salam Abdul Razak, military spokesman of the Free Syrian Army's Nour al Din al-Zinki group.

However, the rebels still need to advance another 2.5 km and take the artillery base, one of the biggest in Syria, in order to reach fellow rebels on the Aleppo side.

The army earlier confirmed on state media that rebels had begun an offensive but said they had been pushed back from the base.

A quarter of a million civilians still live in Aleppo's opposition-controlled eastern neighbourhoods, effectively under siege since the army, aided by Iranian-backed militias, cut off the last road into rebel districts in early July.

The army last week took significant ground on the northern edge of the city, around the Castello road, which leads north towards Turkey.

The British-based Syrian Observatory for Human Rights said the rebel assault was their biggest for several months.

The monitoring group, which tracks violence across Syria, said pro-government jets had bombed rebel-held Khan Touman in the southern countryside of Aleppo, and rebels had shelled government-held parts of central Aleppo overnight.

Aleppo, Syria's biggest city before the outbreak of the conflict five years ago, has been divided between government forces and rebels since the summer of 2012.

Seizing full control would be the biggest victory for Syrian President Bashar al-Assad in five years of fighting, and demonstrate the dramatic shift of fortunes in his favour since Moscow joined the war on his side last year.

Assad's government and its Russian allies declared a joint humanitarian operation for the besieged area on Thursday, bombarding it with leaflets telling fighters to surrender and civilians to leave.

But the United Nations raised misgivings about the plan and U.S. officials suggested it might be an attempt to depopulate the city so that the army can seize it.

(Reporting by Suleiman Al-Khalidi, Additional reporting by Lisa Barrington; Editing by Kevin Liffey)