President Donald Trump said Tuesday he had ordered more robust "extreme vetting" of travelers coming into the United States following the first deadly attack in New York blamed on terror since the September 11, 2001 strikes.

"I have just ordered Homeland Security to step up our already Extreme Vetting Program. Being politically correct is fine, but not for this!" Trump tweeted.

The president's attempts at banning travelers from several mainly Muslim nations have been met with successive legal challenges.

His administration announced last week that it would resume accepting refugees after a 120-day ban, though arrivals from 11 "high-risk" countries, most of them home to Muslim majorities, will still be blocked