Trump, who has long advocated tougher screening of immigrants and other policies designed to prevent terrorism in the United States, did not specify which vetting program he was referring to or how it would change under his Tuesday order. White House officials had no immediate comment to explain the president's tweet.
It appeared Trump was referring to the U.S. government's vetting programs for foreign nationals, as opposed to his controversial travel ban, which affected only a handful of majority-Muslim nations.
Law enforcement officials identified the suspect in Tuesday's attack as Sayfullo Saipov, 29, an Uzbek immigrant who had lived in Tampa and New Jersey.
Uzbekistan was not among the countries named in any version of Trump's travel ban.
In a Monday interview with Fox News host Laura Ingraham, White House Chief of Staff John F. Kelly defined "extreme vetting" as verifying the identities of people traveling to the United States.
“Extreme vetting is, we simply interview people and have to satisfy ourselves that the person we’re talking to is indeed the person who they claim,” Kelly, a former secretary of homeland security, told Ingraham. “It might be impossible to do in some cases.”
Kelly added, “If we can't verify, I don't think we should let them into the country.”