"I think the actions he took certainly justify that," White House press secretary Sarah Huckabee Sanders said, adding that a final determination had not been made.
The designation would mean 29-year-old suspect Sayfullo Saipov could be denied access to a lawyer and detained indefinitely without charge.
It could also open the door to military justice and transfer to the prison at Guantanamo Bay, something Donald Trump said he was willing to consider earlier yesterday.
But amid great controversy, it was the subject of a Supreme Court ruling and would later be abandoned by then President Barack Obama, although some of the provisions would be kept in place.
Supporters say it allows the authorities to detain potentially dangerous terror suspects.
Senator John McCain called for the administration to use the designation.
"We must not consider these attacks on our homeland in isolation, but rather recognise them for what they are: acts of war," he said.
Critics say it is unconditional, erodes individuals' rights and the rule of law, and is open to abuse.
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