Trump said the attacker Sayfullo Habibullaevic Saipov, who ploughed a pickup truck down a crowded bike path near the World Trade Centre killing eight people and injuring 11 others in an ISIS-inspired plot, was allowed to enter the US on a State Department programme known as the "Diversity Lottery Programme".
"I am starting the process of terminating the diversity lottery programme," Trump told reporters ahead of a cabinet meeting.
"All of America is praying and grieving for the families who lost their precious loved ones. Horrible Act. Our hearts break for them and we pledge to renew our resolve in their memory, he said.
Trump called the Uzbek immigrant who carried out the attack an "animal".
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"My administration is coordinating closely between federal and local officials to investigate the attack and to further investigate this animal who did the attacking, he added.
"They'll go through court for years. At the end, who knows what happens. We need quick justice, and we need strong justice. Much quicker and much stronger than we have right now. Because what we have right now is a joke, and it's a laughing stock."
"Im going to ask Congress to immediately initiate or get rid of this programme, he said.
"And we want to get rid of chain migration. This man who came in, or whatever you want to call him, brought in with him other people. And he was the point of contact, the primary point of contact, for and this is preliminary, for 23 people who came in or potentially came in with him. And thats not acceptable, Trump said referring to the attacker.
"Send him to Gitmo, I would certainly consider that," Trump told reporters
He alleged that there are a lot of good bills that are being stopped by Democrats because theyre being obstructionists.
"Terrorists are constantly seeking to strike our nation and it will require the unflinching devotion to our law enforcement, homeland security and intelligence professionals to keep America safe, Trump said.
We have to get much tougher and we have to get much smarter. And we have to get much less politically correct. Were so politically correct that were afraid to do anything, he said.
The programme aims to diversify the origins of people granted permanent residence -- so-called green cards -- in the United States.
Trump said he wants to move US immigration to a "merit- based system" and not allow immigrants to bring their extended families.
Trump has ordered the Homeland Security to step up extreme vetting programme.
In a series of tweets, the president lashed out at Senate Minority Leader Chuck Schumer for opposing merit-based immigration system.
"Senator Chuck Schumer helping to import Europe's problems.. We will stop this craziness!" Trump tweeted.
Schumer, in a statement, said that it was too soon to politicise a tragedy.
"President Trump, instead of politicising and dividing America, which he always seems to do at times of national tragedy, should be focusing on the real solution anti- terrorism funding which he proposed cutting in his most recent budget," Schumer said.
"I'm calling on the president to immediately rescind his proposed cuts to this vital antiterrorism funding," he said.
"This was an act of terror, and a particularly cowardly act of terror aimed at innocent civilians, aimed at people going about their lives who had no idea what was about to hit them," New York Mayor Bill de Blasio said.
The most recent violence from terrorism there came in September 2016, when a man set off shrapnel-packed explosives in the Chelsea neighbourhood of Manhattan. Nobody was killed, but 30 people were injured in the incident.