 -- Russia's military has said Syrian government troops have seized more than 52 percent of the opposition-held east of Aleppo as they continue a relentless offensive that is steadily shrinking the area defended by rebel groups in the city as the government made major gains in the past week.

Russia’s defense ministry said government forces had taken 30 neighborhoods in the eastern part of Aleppo, which has been under total siege since late summer and is suffering relentless bombing. Rebels have refused to surrender as government forces, backed by Iranian and Shiite militias, have surged forward, rejecting Russian calls for them to abandon the city as tens of thousands of people have fled. An official from the rebel group, Jabha Shamiya, confirmed some of the government's advances to Reuters, saying the troops were now approaching Aleppo's Old City.

The retaking of Aleppo, Syria's second largest city, would be a major victory for Syrian president Bashar al-Assad and a severe blow to the rebels who have been seeking to throw off his rule in the 5-year-old conflict. U.S. and European protests about the relentless bombing and advance into the city have had no effect. The U.N. Security Council is set to discuss a draft resolution on Monday calling for a seven-day truce in Aleppo, but Russia may veto it.

Russian officials have said they hope Aleppo will be completely retaken by the end of the year and on Saturday foreign minister Sergei Lavrov called on all rebel fighters "without exception" to lay down their arms and agree to leave the city. Lavrov, speaking in a news conference in Geneva, said Moscow was ready to negotiate the rebel's exit from the city with the United States, which has supported opposition in the city with arms and supplies.

Rebel commanders have rejected the proposal, telling news agencies they want humanitarian corridors to be opened for civilians and the wounded but that they will fight on. A senior rebel official from the Fastaqim group, Zakaria Malahifji told Reuters on Sunday that they had told U.S. representatives they are not prepared to leave.

"Our response to the Americans was as follows: 'We cannot leave our city, our homes, to the mercenary militias that the regime has mobilized in Aleppo,'" he said.

Malahifji, speaking from Turkey, said the U.S. representatives "listened to the response and did not comment."

Secretary of State John Kerry met with Lavrov in Geneva on Friday to discuss the situation in Aleppo. The U.S. had cut off talks with Russia after a ceasefire agreed between the two powers collapsed in mid-September and heavy bombing by Russian and Syrian aircraft resumed.

Lavrov said Kerry had made proposals on Friday that were more "in line with" what Moscow has been suggesting and said that Russia was ready to send negotiators immediately to Geneva to draw up plans with American officials on how to have rebels withdraw from Aleppo. The U.S. has not said whether it is considering that scenario.

On Friday, Kerry said the U.S. is exploring new options with Russia for helping civilians leave Aleppo, where the U.N. estimates between 100,000 and 200,000 people may be trapped, with the goal of potentially clearing a path to fresh negotiations to halt fighting in Syria more broadly later.

"If indeed we could create a framework for the passage of people out of Aleppo so that Aleppo itself might be able to be relieved from this agony, that could open up the space to perhaps to be able to start some kind of conversation in Geneva," Kerry said at a news conference, warning however that it was unclear if the Assad government was prepared to cooperate in that.

U.S. officials are expected to discuss the issue again with Russian representatives in Germany next week.

Conditions for civilians in Aleppo are dire, with daily bombing and near-constant shelling, while food and medical supplies are running desperately short. All hospitals rebel-held territory have been destroyed or severely damaged, according to the World Health Organization. The International Committee of the Red Cross estimates that at least 30,000 people have fled the shattered city in the past week, adding to the 400,000 people who were already forced from their homes.

"The destruction is indescribable -- the limbs, burnt limbs. Buildings collapsed and were burned down, mosques were destroyed completely," Khalil Halabi, 35, a pharmacist fleeing eastern Aleppo told Reuters.