The brothers, who say they are innocent, are accused of having formed an organised criminal network in early 2021 in Romania, as well as in the US and Britain
The statement did not specify the timing of the operation, how his long-rumoured death had been confirmed, or even specifically in which country it occurred.
US Senator Lindsey Graham, a Republican, welcomed the development, saying on Twitter that it sent "a strong signal that America never forgets and we will go wherever the terrorists take us to protect our homeland."
Hamza, the 15th of Osama bin Laden's 20 children and a son of his third wife, was "emerging as a leader in the Al Qaeda franchise," the State Department said in announcing a $1 million bounty on his head in February 2019.
It said Hamza was married to a daughter of Abdullah Ahmed Abdullah, a senior Al Qaeda leader indicted by a US federal grand jury in 1998 for his role in the bombings that year of US embassies in Tanzania and Kenya - attacks overseen by the senior Bin Laden.
"But obviously he's got the DNA - the Bin Laden name," he told AFP.
Al Qaeda has yet to confirm the US announcement.
Barak Mendelsohn, a political science professor and terror specialist at Haverford College, called it "surprising" that so long after Hamza's death was first reported, "Al Qaeda has yet to release a formal announcement with details about how he died, and a eulogy."
Osama bin Laden's death and the rise of the more virulent Daesh group saw Al Qaeda lose currency with younger jihadists. But the proliferation of associated groups in Afghanistan, Yemen, Syria and elsewhere has underscored its continuing potency.
"The unknown actually is what's more dangerous," he said.
"The reality is that while Hamza was being groomed as a potential replacement for Al Zawahiri, the group could never focus on grooming only one potential heir," he said.
"They cannot predict who will actually be alive when Al Zawahiri departs the scene."
The brothers, who say they are innocent, are accused of having formed an organised criminal network in early 2021 in Romania, as well as in the US and Britain
The left-handed batter scored 3369 runs in 136 one-day internationals and 2893 in 140 Twenty20 internationals — both Pakistan records
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The charges against them include planning terrorist acts, fundraising for the Organisation, and concealing the source and destination of those funds