The U.S. Treasury Department said four other individuals were also sanctioned, as was the group ISIS in the Greater Sahara, which was designated as a foreign terrorist organization.
It was the third round of sanctions announced by Washington since the United States pulled out of the Iran nuclear deal last week.
Wednesday's sanctions targeted members of the primary decision-making body of Hezbollah, Treasury said in a statement.
"By targeting Hezbollah's Shura Council, our nations collectively rejected the false distinction between a so-called 'Political Wing' and Hezbollah's global terrorist plotting," Treasury Secretary Steven Mnuchin said.
The move expands U.S. sanctions against Nasrallah, who was sanctioned by Washington in 1995 for threatening to disrupt the Middle East peace process and again in 2012 over Syria. It is, however, the first time that the U.S. Treasury has acted against Qassem, who is being listed for his ties to Hezbollah.
The measures were imposed jointly by Washington and its partners in the Terrorist Financing and Targeting Center (TFTC), which includes Saudi Arabia, Bahrain, Kuwait, Oman, Qatar and United Arab Emirates, it said.
The Gulf states targeted four of the movement's committees and ordered individuals' assets and bank accounts frozen.
A number of those targeted by the TFTC had been previously blacklisted by the United States.
Nasrallah last year dismissed the prospect of tougher U.S. sanctions against his group.
"The American administration, with all available and possible means, will not be able to damage the strength of the resistance," Nasrallah said on Aug.13 in a televised address to mark the anniversary of the end of Hezbollah's 2006 war with Israel.
Shi'ite Hezbollah was formed to combat Israel's 1982-2000 occupation of Lebanon. It and its political allies made significant gains in Lebanon's parliamentary election earlier this month, boosting an Iranian-backed movement fiercely opposed to Israel and underlining Tehran's growing regional clout.
The Trump administration has sought in recent days to choke off funding for Iran's overseas operations, including its backing for Hezbollah, in what Washington says are its malign activities in the Middle East.
On Tuesday, the U.S. Treasury imposed sanctions on Iran's central bank governor and an Iraq-based bank for funneling millions of dollars on behalf of Iran's elite revolutionary guards.
Last week, the U.S. Treasury imposed sanctions against six individuals and three companies it said were funneling millions of dollars to the Revolutionary Guard's external arm, Quds Force.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)
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