Aleppo, Beirut: Russia's Defence Ministry said on Monday that 728 Syrian rebels laid down their weapons over the past 24 hours and relocated to western Aleppo.
The Defence Ministry also said that 13,346 civilians left rebel-controlled districts of Aleppo over the same period.
Syrian rebels, meanwhile, have received a US-backed proposal to leave Aleppo along with civilians under safe passage guaranteed by Russia, rebel officials said as government forces closed in on Sunday, but Moscow denied a deal had been reached.
If the proposal were to be taken up by all sides, it would end four years of fighting in the city, and months of siege and intense bombardment that have created a humanitarian crisis - particularly in rebel territory that has now shrunk to a small pocket crammed with civilians.
Three officials with insurgent groups in Aleppo told Reuters that a letter outlining the proposal had been received, offering an "honorable" departure for the rebels to a place of their choice.
Rebel groups have yet to respond. But if fully accepted, the proposal would give Syrian President Bashar al-Assad and his military coalition of Russia, Iran and Shi'ite militias their greatest triumph in the civil war against the rebels who have fought for nearly six years to unseat him.
However, the sudden recapture by the Islamic State of the ancient desert city of Palmyra on Sunday after a much-trumpeted army victory there in March has shown how difficult Assad may find it even after Aleppo to restore his rule across Syria.
Asked whether they had been contacted by the United States and Russia over talks between the two powers in Geneva to find a way out of the crisis, one of the officials with rebel groups that are present in Aleppo said:
"They sent us a letter, they are saying to safeguard the civilians ... you can leave in an honorable way to any place you choose and the Russians will pledge publicly that nobody will be harmed or stopped," said one of the officials. "We have yet to give a response."
A second official said a document "is being proposed to the factions, the fundamental thing in it is the departure of the all the fighters in an honorable way".
However, Russia swiftly said it had not reached any agreement with the United States on a proposal to withdraw fighters from Aleppo and added that the Geneva talks were continuing.
Moscow was working to create the necessary conditions for the safe extraction of people from Aleppo, said Russian Deputy Foreign Minister Sergei Ryabkov.
"The issue of withdrawing militants is the subject of separate agreements. This agreement has not yet been reached, largely because the United States insists on unacceptable terms," he said in comments reported by RIA news agency.
United Nations special Syria envoy Staffan de Mistura had no comment on the report, but some were skeptical that the proposal could succeed. "With all previous commitments reneged on by (the Syrian) regime/Russia it is difficult to see how rebels are to trust this offer of safe exit," one former Western envoy in Syria told Reuters in Geneva.
As the army swept through east Aleppo in the past two weeks, taking three quarters of rebel ground, tens of thousands fled the fighting, some to government-held areas and others deeper into the insurgent pocket.
Daesh ‘retake’ Palmyra
New army gains on Sunday south of Aleppo's historic citadel appeared to bring victory closer for Assad, with a rebel official saying world powers seemed to be presenting his side with a choice of "death or surrender".
The Daesh attack on Palmyra, 200 km (120 miles) to the southeast, threatens to inflict a serious blow on both Damascus and Moscow.
Syrian state radio reported the army had evacuated its positions inside Palmyra, whose Roman-era ruins have become an emblem of the conflict. They were redeploying around the city.
Analysts have warned that even if Assad defeats the main rebellion, he may still face years of guerrilla insurgency and bombing attacks as he tries to reassert his authority.
Daesh, the so-called Islamic State, seized Palmyra in May 2015, one of its last major conquests after nearly a year of advances in Syria and neighbouring Iraq that took advantage of the region's chaos.
Its destruction of some of the best-known ruins and killing of the leading archaeologist in the city provoked global outrage and the army's recapture of Palmyra was presented by Damascus and Moscow as vindicating Russia's entry into the war.
Daesh has suffered a string of setbacks since late last year, losing its once long stretch of territory on the border with Turkey, an important source of supplies and recruits, as well as the city of Manbij.
The group is fighting an assault on its most important possession in Iraq, the city of Mosul.
It is also under attack north of Raqqa, its Syrian capital, following a series of air strikes that have killed some of its most important leaders.
Russian news agencies reported that air strikes had killed 300 militants overnight near Palmyra but that more than 4,000 fighters had still managed to launch the attack on the city.
Under the terms of the proposed deal, rebels could leave Aleppo with light weapons. It would be implemented over a 48-hour period and oversight would be sought from the UN.
Fighters from the hardline group Jabhat Fateh Al-Sham, formerly known as the Nusra Front until it broke allegiance to Al Qaeda in July, would have to go to Idlib.
Other fighters could choose separate destinations, including near the Turkish border northeast of Aleppo.
There was no immediate comment from Damascus on the proposal.
Heavy shelling and air raids pounded Aleppo's rebel enclave from midnight on Saturday and throughout Sunday morning, a Reuters reporter in the city said, with explosions at a rate of more than one a minute. Gunfire was also heard.
Thousands of refugees are still pouring from Aleppo's areas of fighting. The Syrian Observatory for Human Rights, a war monitoring group, said more than 120,000 civilians had left the eastern part of the city as the government advance closed in, but that tens of thousands remained.
The mostly Sunni rebels include groups supported by the United States, Turkey and Gulf countries, but also some hardline militant factions that receive no assistance from the West.
The army seized the Al-Maadi district on Sunday morning before rebels were able to return and continue fighting there, said the Jabha Shamiya official.
A Syrian military source said the army and its allies had captured the Al-Asila and Aaajam districts, southeast of Aleppo's ancient citadel, as well as the southern portion of the Karam Al-Daadaa neighborhood.
The Observatory also said the army had advanced in those areas.
Reuters reporters on a tour of Old City districts captured by the army saw how its historic covered market had been pounded, with ancient quarters reduced to a warren of defensive positions daubed with rebel slogans.
"Embrace death for Aleppo" was one.
State television showed footage of the east Aleppo fighting: a tank moving slowly along a street as soldiers ran alongside it, smoke and dust billowing around them.