"The terrorist came into our country through what is called the 'Diversity Visa Lottery Program,' a Chuck Schumer beauty. I want merit based," Trump told media and tweeted.
Five Argentine and a Belgian were among the eight dead in the Manhattan terror attack.
"We are fighting hard for Merit Based immigration, no more Democrat Lottery Systems. We must get MUCH tougher (and smarter)," said Trump.
The suspect, Sayfullo Saipov, 29, became a US citizen from Uzbekistan reportedly through the diversity visa program.
Media reports quoting authorities said the suspect was “associated with ISIS".
The five member Argentine group that were killed in the truck attack were celebrating the 30th anniversary of their high school graduation, the Argentine Foreign Ministry said in a statement Tuesday.
The ministry has identified them as Hernán Mendoza, Diego Angelini, Alejandro Pagnucco, Ariel Erlij and Hernan Ferruchi.
At least eight people were killed as the trucker ran over them in New York's Lower Manhattan area.
The deadly incident also left 11 gravely injured.
Reports quoted witnesses as saying that he shouted Allahu Akbar before killing the pedestrians.
Trump condoled the loss and tweeted, "My thoughts, condolences and prayers to the victims and families of the New York City terrorist attack. God and your country are with you!"