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Russian and U.S. officials are meeting in Geneva on Sunday for more talks on an elusive deal for civilians and fighters to leave the city, diplomats said, but the rebel official said the Aleppo insurgents had had no word yet on their progress.
The fall of all of Aleppo to President Bashar al-Assad would bring him the biggest victory yet after nearly six years of civil war, but he would still remain far from restoring government control over his country.
More than 200 miles (120 miles) away, Islamic State staged a surprise advance on the city of Palmyra over the weekend despite losing ground elsewhere in the country, showing how volatile the fortunes of war are and how stretched the army and its allies are.
The Syrian Observatory for Human Rights, a war monitor, said the militants had recaptured the ancient city on Sunday after briefly retreating in the face of heavy Russian air strikes.
Heavy shelling and air raids pounded Aleppo's besieged rebel pocket 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.
"The result will certainly be a complete end of the district, in a tragic way," said the Turkish-based official from the Jabha Shamiya rebel group, which is present in Aleppo.
Thousands of refugees are still pouring from the areas of fighting. The Observatory said on Sunday that 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.
Assad's forces are supported by Russian air power, Iran and Shi'ite militias from Lebanon, Iraq and Afghanistan. Together they have helped to turn the tide of conflict his way after he seemed to be on the back foot in mid-2015.
The mostly Sunni rebels include groups supported by the United States, Turkey and Gulf monarchies, but also some jihadist 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 neighbourhood.
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 adorned 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.