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Mr Wray said information suggests Hamas does not intend to operate inside the US, but the FBI is not discounting those inspired by the group.
Jewish US citizens and Arab Americans in particular have become targets.
“We have seen violent extremists across ideologies seeking to target Jewish and Muslim people and institutions through physical assaults, bomb threats and online calls for mass casualty attacks,” Mr Wray told the US Senate homeland security and government affairs committee.
Lone actors inspired by the Hamas attacks pose the most likely threat to Americans, he said.
“Especially Jewish, Muslim, and Arab American communities in the United States,” Mr Wray said.
Hamas has been designated as a terrorist organisation by the US since 1997.
He spoke of the fatal stabbing of Wadea Al Fayoume, a six-year-old Palestinian boy.
The suspect, Joseph Czuba, faces murder and hate crime charges from the attack and for critically wounding the boy's mother, Hanaan Shahin.
Mr Wray also said a man in Houston was arrested for posting about “killing Jews”.
“The continuing war in the Middle East has raised the threat of an attack against Americans in the United States to a whole other level,” he said.
During the hearing, Homeland Security Secretary Alejandro Mayorkas issued a similar warning that lone actors pose the most likely threats.
“As the conflict continues, we have seen an increase in reports of threats against Jewish, Muslim and Arab-American communities and institutions,” he said.
Mr Mayorkas, whose mother is a Holocaust survivor, said that hate directed at the Jewish community since the October 7 Hamas attack adds “to a pre-existing increase” in anti-Semitism domestically and globally.