ALEPPO, Syria/BEIRUT (Reuters) - The Syrian army pressed an offensive in Aleppo on Friday with ground fighting and air strikes in an operation to retake all of the city’s rebel-held east that would bring victory in the civil war closer for President Bashar al-Assad. “The advance is going according to plan and is sometimes faster than expected,” a Syrian military source told Reuters. The Syrian army and its allies had recaptured 32 of east Aleppo’s 40 neighborhoods, about 85 percent of the area, he said. Reuters journalists, rebels and a monitor confirmed the military thrust. There were no reports the Syrian army had made significant gains. Russia’s Foreign Minister Sergei Lavrov said the Syrian army had suspended military activity to let civilians leave rebel-held areas, RIA news agency reported.       The army and its allies tried to advance on two fronts, a Turkish-based official with the Jabha Shamiya rebel group said. “Helicopters, warplanes and rocket bombardment like every day. Nothing has changed,” the official said. Despite the bombardment, “the guys are steadfast,” the official added. During a tour of Old Aleppo on Friday, which the Syrian army took control of this week, Reuters journalists counted the sound of nine air strikes in about half an hour. Fighting could be heard from other areas nearby.  The Russian air force and Iran-backed Shi’ite militias are fighting in Aleppo on the government side. Rebel leaders have given no sign they are about to withdraw as the civilian population is squeezed into an ever-decreasing area. Russian Defense Ministry official Sergei Rudskoi said on Friday up to 10,500 Syrian citizens had fled parts of east Aleppo still controlled by rebels in the last 24 hours. This could not be independently verified. Syrian government and allied forces have in the last two weeks driven rebels from most of their territory in what was once Syria’s most populous city. The rebels have controlled the eastern section since 2012, and Assad said in an interview published on Thursday that retaking Aleppo would change the course of the civil war across the whole country. The Syrian government now appears closer to victory than at any point in the five years since protests against Assad evolved into an armed rebellion. The war has killed more than 300,000 people and made more than half of Syrians homeless. Outside of Aleppo, the Syrian army declared a ceasefire in several areas around Damascus and the northwestern province of Idlib beginning on Friday evening, without saying how long it would last. There was no immediate comment from rebels. But there was no sign of any such truce inside Aleppo. “There are aerial raids on the city’s neighborhoods with highly explosive incendiary bombs, barrel bombs and artillery shelling,” a fighter with the Nour al-Din al-Zinki rebel group on an eastern Aleppo frontline told Reuters.    In Old Aleppo, newly recaptured by the government, there was widespread destruction in the UNESCO World Heritage Site, with fire-damaged ancient buildings, structures reduced to rubble and spent ordnance everywhere.  At the side of a road sat a woman in her late 20s, veiled, dressed in black, and weeping as she cradled her baby. “My son was born after three months of siege. There were no hospitals, no diapers, no milk,” she said. “My milk is dry from fear and panic.”  Dozens of displaced civilians, including children, had gathered in the road with their belongings after fleeing the Saliheen district, where battles continued.  Maher Tashtash, aged nine, said the bombardment had been frightening and rebels had told them they faced death if caught by the army. His brother Mohammed, 12, said they had hidden in a cellar until the fighting passed.  Even the dead were not spared the carnage. In the Dar al-Islam cemetery near Ibn Sina street in al-Hamdaniya, graves were destroyed. People were burying corpses in open public ground. The United Nations estimates about 100,000 people are now squeezed into an “ever shrinking” rebel-held pocket of Aleppo with virtually no access to food, water or medical care. In rebel-held Aleppo, a Reuters journalist said there were intense clashes on Friday in Sheikh Saeed district in the south of the eastern sector, where the Observatory and a Syrian military source said government forces advanced on Thursday. Fighting also took place northeast of Aleppo, where Turkey has intervened to support rebels against both Islamic State fighters and Kurdish groups. Turkish-backed rebels closed in on the Islamic State-held city of al-Bab with Turkish tanks and warplanes supporting the assault, Turkish foreign minister Mevlut Cavusoglu said. Moscow and Washington have discussed a ceasefire to let civilians escape eastern Aleppo and aid enter. Russia also wants the United States to urge rebel fighters to abandon their territory and accept transport out. U.N. envoy to Syria Staffan de Mistura told the Security Council on Thursday there were signs fighters in Aleppo may want to leave and the council should help them go, diplomats said.  The Syrian government said on Friday it was ready to resume dialogue with the opposition, without external intervention or preconditions. Rebels said no such contacts were taking place. “There are no negotiations now, except what’s being discussed internationally,” said Zakaria Malahifji, head of the political office of the Aleppo-based Fastaqim rebel group, speaking from Turkey. “We have asked for the evacuation of civilians who want to leave and of the injured. The fighters are determined to stay and face things.” U.S. and Russian officials will meet in Geneva on Saturday to discuss Aleppo, State Department spokesman Mark Toner said in a news briefing on Friday. The talks will focus on achieving a pause in the fighting, the delivery of humanitarian aid to civilians, and ensuring a safe departure for those who want to leave, Toner said. U.S. Secretary of State John Kerry, who has invested months of intensive diplomacy on Syria, acknowledged the exasperation many feel. “I know people are tired of these meetings. I’m tired of these meetings. ... what am I supposed to do? Go home and have a nice weekend in Massachusetts while people are dying?” Kerry said at the U.S. embassy in Paris, according to a State Department transcript. “What is happening in Aleppo is the worst catastrophe – what’s happening in Syria is the worst catastrophe since World War Two itself. It’s unacceptable. It’s horrible.” The U.N. General Assembly voted 122 to 13 on Friday to demand an immediate cessation of hostilities in Syria, humanitarian aid access throughout the country and an end to all sieges, including in Aleppo. General Assembly resolutions are non-binding but can carry political weight. The European Union said on Friday it would introduce more sanctions on Syrian individuals and entities over the Aleppo offensive. The U.N. human rights office said hundreds of men from eastern Aleppo were missing after leaving rebel-held areas, voicing deep concern over their fate at the hands of government forces. The government has dismissed reports of mass arrests, torture and extrajudicial killings by its forces as fabrications. Rebels for their part deny they have prevented civilians from leaving opposition-controlled areas. 