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The Act gives the President the right to block or revoke the visas or impose property sanctions on them.
"It is imperative that any individuals or entities responsible for atrocities, including non-state actors and vigilantes, be held accountable," the statement further said.
Since August 25, Myanmar's powerful army has launched a military campaign against the Rohingya.
More than 600,000 Rohingya have fled the country to walk by foot or sail in rickety boats to arrive in neighbouring Bangladesh.