By Yeganeh Torbati

WASHINGTON (Reuters) - The U.S. government on Tuesday imposed sanctions on three leaders of the militant group Hezbollah and a businessman in Lebanon, saying they were key players in the group's military operations in Syria.

The sanctions were imposed by the U.S. Treasury Department.

"The United States will continue to aggressively target (Hezbollah) for its terrorist activities worldwide as well as its ongoing support to (Syrian President Bashar al-) Assad's ruthless military campaign in Syria," said Adam Szubin, the Treasury Department's acting under secretary for terrorism and financial intelligence.

U.S. President Barack Obama and Secretary of State John Kerry have said they are troubled by support from Iran for regional proxy groups such as Hezbollah.

The United States and world powers struck a deal with Iran last week to limit the country's nuclear program in return for relief from sanctions. Obama said last week that the deal would make it easier for the United States to "check Iran's nefarious activities."

The Treasury said it had taken action in June against Hezbollah front companies.

Hezbollah has long been designated a terrorist organization by the United States, but Tuesday's action was directed at three senior military officials - Mustafa Badr Al Din, Ibrahim Aqil, and Fu'ad Shukr - for their role in coordinating or participating in the group's support for Assad's government in Syria's ongoing civil war.

A businessman in Lebanon, Abd Al Nur Shalan, was also sanctioned for procuring weapons for Hezbollah and shipping them to Syria, the Treasury Department said.

(Reporting by Yeganeh Torbati; Editing by Sandra Maler, Toni Reinhold)