Trump added that the attack was carried out "by a very sick and deranged person".
A law enforcement official identified the driver as 29-year-old Sayfullo Habibullaevic Saipov.
Trump's reaction "is in keeping with his responses to other attacks" in which the perpetrator was alleged to have possible links with Islamic State, says Al Jazeera English. "Thoughts & prayers as we monitor the situation".
National security and public safety information that focuses on whether the originating country "makes available, directly or indirectly, known or suspected terrorist and criminal-history information upon request, whether the country provides passport and national-identity document exemplars, and whether the country impedes the United States Government's receipt of information about passengers and crew traveling to the United States".
President Trump has called for tougher immigration controls after the deadly NY truck attack, describing the suspect as an "animal" and calling on Congress to shut down the immigration lottery scheme. "God and your country are with you!" "We need to first see what plan Washington would put in place before commenting on the development", a government source said on condition of anonymity.
At a press briefing, New York City mayor Bill de Blasio and New York governor Andrew Cuomo condemned the attack as an act of terrorism but urged New Yorkers not to be afraid of further attacks. "We are not going to be deterred".
Cuomo echoed him in more vigorous terms, saying: "We go forward together. If we can't verify, I don't think we should let them into the country".
Cuomo ordered increased security at New York's airports, bridges, tunnels, and mass transit systems, and directed that the lights on the spire of 1 World Trade Center be lit in red, white, and blue in honor of "freedom and democracy".
Police said the vehicle entered the bike path at about 3 p.m. on West Street a few blocks from the new World Trade Center, the site of the deadliest terror attack in United States history.
"As the investigation unfolds, it's critical that we learn what we can from this incident and do everything we can to prevent this from happening again". He later gave a speech that warned that terrorists were being allowed to flow into the USA because of a failed immigration system and delivered a speech unveiling his proposals for "extreme vetting".