Trump said his administration would seek to end what he called "chain migration," and institute "a merit-based program, where people come into our country based on merit."
Trump made the comments during the meeting in the White House, where he also said he would consider sending Saipov to the military detention center at Guantanamo Bay, Cuba, while he awaits trial.
Saipov is suspected of using a rented truck on Tuesday to kill eight people in lower Manhattan, an attack that authorities have described as an act of terror inspired by ISIS.
Officially known as the Diversity Visa Lottery, the green-card lottery was written into law in 1990 and went into effect in 1995. Under the program, approximately 50,000 visas are awarded annually to applicants from parts of the world that are typically underrepresented in U.S. immigration.
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