The fighters were helping Syrian forces loyal to President Bashar al-Assad, backed by Russian air power, as they opened a new front against rebel fighters southeast of Aleppo.
"We are now seeing a coordinated effort between Iran and Russia to assist Assad with fighting opposition groups," the official said, speaking on condition of anonymity.
"There could be as many as 2,000 Iranian-enabled forces," he added.
The official defined those forces as consisting of Iranians including Quds special forces, Iranian-funded proxies and Lebanese Hezbollah, noting it was difficult to determine a precise number of fighters.
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Russians at the time denied Soleimani had visited Moscow.
Colonel Pat Ryder, the spokesman for the US military's Central Command, said there were clear "indications" Iranian forces were in Syria.
"We have seen where Iranian forces are cooperating with Syrian regime forces," Ryder said.