ALEPPO, Syria/BEIRUT (Reuters) - Syria’s military and Russian warplanes bombarded rebel-held districts of Aleppo on Saturday as Damascus’s allies said victory was near, but insurgents fought back and army advances halted after rapid gains during the week.

The United States said it was meeting a Russian team in Geneva to find a way to save lives, but an agreement looked elusive as the two countries, which back opposing sides, have repeatedly failed to strike a deal to allow evacuations and help aid deliveries.

Russia, whose military intervention helped turn the war in President Bashar al-Assad’s favor, said the Syrian government now controls 93 percent of Aleppo, a figure Reuters could not independently verify. Recapture of the country’s second-largest city would deal a major blow to rebels who have fought to unseat Assad in the nearly six-year war.

The insurgents are holed out in a handful of areas mostly south of the historic Old City, having lost nearly three-quarters of territory they controlled for years in the space of around two weeks.

Lebanese Shi’ite group Hezbollah, a key military ally of Damascus alongside Russia and Iran, said late on Friday that a “promised victory” in Aleppo was imminent and would change the course of the war.

The advances mean the government appears closer to victory than at any point since 2011 protests against Assad evolved into armed rebellion. The war has killed more than 300,000 people and made more than 11 million homeless.

A win for Assad in Aleppo looks close, but the fighting still raged on Saturday.

In a surprise setback elsewhere, government forces lost control of most of the ancient city of Palmyra in eastern Syria to Islamic State, a war monitor and rebels said. [L5N1E506M]

The army earlier said it had sent reinforcements to Palmyra, more than 200 kms (130 miles) away, to stave off a fierce attack by the militants.

A rebel commander in the Aleppo-based Jaish al-Mujahideen group said the IS offensive had forced the government to divert troops to Palmyra from Aleppo - a possible explanation for the slowed advance there and heavy aerial and artillery bombardment.

Russian warplanes and Syrian artillery bombarded rebel-held districts, and rebels responded with shelling of government-controlled areas as gunfire rang out, a Reuters correspondent in Aleppo said.

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Russia and Syria said on Friday they had reduced military operations to allow civilians to leave.

But rebels said their counterattacks are what have halted government advances.

“There’s no advance by the regime. They (rebels) have stopped them several times,” Zakaria Malahifji, a Turkey-based official in the Fastaqim rebel group said.

VAST DESTRUCTION

Fighting has killed hundreds of people in recent weeks, monitors say, and devastated large areas of east Aleppo.

Parts of the UNESCO World Heritage Old City recaptured by the government were completely destroyed by fighting, a Reuters correspondent said. Old markets and bathhouses had been flattened.

“I found my home destroyed,” said one returning resident, who gave only his family name, Sheikho.

“I didn’t even recognize where it was because of the destruction,” he said.

Mohammed Shaaban, standing outside a destroyed church, was also astounded by the destruction.

“A year and a half ago when I last visited there was not this level of damage. I’m shocked and saddened. They destroyed civilization and humanity,” he said, referring to rebels.

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The Syrian Observatory for Human Rights monitoring group said several people were killed in rebel shelling on Saturday.

Thousands of people have left rebel districts. Some have fled to government-held areas but others went to areas under rebel control fearing arrest and reprisals by government forces.

U.S. Secretary of State John Kerry urged Russia to show “a little grace” when American and Russian officials meet in Geneva later on Saturday to try to reach a deal enabling civilians and fighters to leave Aleppo.

“Fighters ... don’t trust that if they agreed to leave to try to save Aleppo that it will save Aleppo and they will be unharmed,” Kerry told reporters in Paris after a meeting of countries opposed to Assad.

“The choice for many of them ... is to die in Aleppo, die in (neighboring) Idlib, but die,” he added.

Germany said Syrian opposition backers were seeking a political solution, but there was no agreement in Paris on a truce.

IS ASSAULT STRETCHES ARMY

Russia’s defense ministry said more than 20,000 civilians left eastern Aleppo on Saturday and over 1,200 rebels laid down their arms. The British-based Observatory said hundreds of civilians had left but no fighters surrendered.

Rebel officials have sworn they will never leave.

The army said that it reduced operations to allow residents to leave and that this would enable the military to carry out “wider maneuvers” against insurgents in due course.

Even once Aleppo is retaken, the multi-sided Syrian war will continue.

The United States, which is leading a separate fight against Islamic State in northern and eastern Syria, said it will send 200 additional military personnel including special forces to create pressure on the group’s Raqqa hub.

The fight against Islamic State, waged separately by the group’s many enemies - Moscow and Damascus, the U.S. coalition, and some of the same Turkish-backed rebels fighting Assad in Aleppo - is just one sign that Syria’s complex conflict will not end with a defeat for insurgents in Aleppo.

Kerry warned the war would create more jihadist militants and grind on.

“If Aleppo were to fall ... the war does not end, but in fact could create more jihadis and more people to seek revenge and prosecute their interests,” he said.