Aleppo has almost entirely fallen to Syrian government forces, state media and Russian officials said Monday after a sustained attack on rebel-held areas packed with civilians.

Syria's military said pro-government forces now control of 98 percent of eastern Aleppo, including the neighborhood of Fardous which has been held by the rebels since 2012.

Lieutenant General Zaid al-Saleh said the battle for the city was entering its final stages.

"The battle in east Aleppo should end quickly," he told a group of reporters in the recaptured Sheikh Saeed district, according to Reuters. "They [rebels] don't have much time. They either have to surrender or die."

Government forces already control the west of Aleppo and recapturing the city —Syria's biggest, before the war — would be the greatest prize so far for President Bashar al-Assad in the six years of conflict.

However, swaths of the country remain in rebel hands and ISIS on Sunday seized the historic city of Palmyra.

A statement Monday from Russia’s military wing in Syria gave a similar account, saying: “Over the past 24 hours, the Syrian government army has liberated three more districts of eastern Aleppo: Sheikh Saeed, Karim Khum and Al-Maqamat.”

It said Syrian authorities were in “full control” of most of the city, adding: “The territory still controlled by the militants in eastern part of the city is no more than [4 square miles].”

It added that more than 5,100 residents have returned to their homes in western districts.

Pro-government forces inspect a building in eastern Aleppo Sunday after retaking it from rebel fighters. GEORGE OURFALIAN / AFP - Getty Images

Rebel forces and tens of thousands of civilians are no squeezed into a handful of central neighborhoods.

Syrian state television broadcast pictures of civilians fleeing areas where troops were advancing, pouring into western Aleppo. Those areas are only accessible through government-monitored crossing points.

The Russia-backed offensive, which began on Nov. 26, followed an intensive aerial bombing campaign that knocked out most of the eastern sector's medical facilities, targeted civil defense and municipal vehicles and blocked roads with rubble. The eastern Aleppo area has also been cut off from outside aid since July by a government siege.

Separately, Syria’s humanitarian White Helmets said Sunday they rescued an eight-month-old baby girl called Fatima from rubble in Saraqeb, near the city of Idlib. No further information was immediately available.