BEIRUT — Syrian troops backed by Russian air power on Thursday appeared close to storming Islamic State-held Palmyra, an ancient city whose capture by the extremist group in May shocked the world.

Retaking the desert city would represent a significant victory for Russia’s military intervention in the conflict in support of President Bashar Assad, a longtime ally.

Syrian state media reported that ground forces have advanced past the outskirts of Palmyra, a UNESCO World Heritage Site about 150 miles northwest of the capital, Damascus. The Islamic State has destroyed several of the city’s Roman-era monuments.

State television said troops have battled their way inside the city, although the Syrian Observatory for Human Rights, a Britain-based monitoring group, said fighting is still at the edges.

The Islamic State’s Amaq News Agency, however, released a video purporting to show quiet in Palmyra, including empty streets. The group “will deter their assault,” a fighter shown sitting on top of a tank says in the video, which was translated by the SITE Intelligence Group.

Meanwhile, Secretary of State John F. Kerry met with Russian President Vladimir Putin at the Kremlin to discuss a political transition for Syria that the Obama administration has said must result in Assad’s exit from power. Putin has firmly pushed back against such a scenario.

“We agreed on a time schedule to establish a framework for a political transition and also a draft constitution, all of which we target by August,” Kerry said at a news conference with Russian Foreign Minister Sergei Lavrov.

Earlier in the day, Kerry and Lavrov praised a mutually backed cease-fire agreement that took hold in Syria on Feb. 27. That truce excludes the Islamic State and has held despite numerous violations reported by each side, helping to reduce violence in a war that has killed more than 250,000 people and uprooted millions.

Putin thanked Kerry and President Obama for their support in achieving progress in finding a resolution to the conflict in Syria.

In Geneva, U.N. envoy Staffan de Mistura concluded nearly two weeks of what he described as “very serious” discussions with the Syrian government and opposition representatives over the “principles” that will guide the political transition that he said would be the topic of talks scheduled to resume early next month.

De Mistura presented both sides with a 12-point document of what he called “points of commonalities” between them.

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