REYHANLI, Turkey—Syrian government forces have nearly encircled Aleppo, preparing a siege to wrest control of the city from rebels in what would be the biggest blow yet to the three-year uprising.

The fall of Aleppo, Syria's largest city and economic hub before the fighting, could also bolster the ranks of Islamic State militants who continue to make gains across the country, as defeated members of the Western-backed Free Syrian Army switch to their side.

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