Donald Trump has insisted Islamic State cannot be allowed to return to the US in the aftermath of the attack in New York City.
Eight people were killed and at least 11 injured after a truck was driven into pedestrians on West Street in lower Manhattan.
The suspected driver - who was identified by officials as 29-year-old Uzbekistan national Sayfullo Saipov - was shot by NYPD officers and taken to hospital in police custody.
The US President posted a string of tweets in the wake of the attack, which has been reportedly attributed to Islamic State based from a note found in Saipov's truck by the authorities.
Among announcements of stepped up vetting procedures, he labeled Saipov "sick and deranged" and insisted Islamic State fighters must not be allowed to return to US soil.
The terror group has not officially claimed responsibility for the incident.
The attack has drawn international condemnation from the likes of Irish Taoiseach Leo Varadkar, British Prime Minister Theresa May, and French President Emmanuel Macron.