“I am starting the process of terminating the diversity lottery programme. We have to do what's right to protect our citizens. We will get rid of this lottery programme as soon as possible,” Trump told reporters.
The 1990 programme awards United States (US) permanent resident visas to around 50,000 applicants from around the world each year, opening the door as well for members of their broader families to follow them, so-called chain migration.
According to Trump, Sayfullo Saipov, who ploughed a rented truck into cyclists and pedestrians on a New York City bike path on 31 October, came to the country via the programme.
Saipov was arrested after being shot by the Police and officials said that he had planned to undertake his attack in the name of the Islamic State for weeks, following online instructions from the jihadist group.
Trump's threat would further close the doors to hopeful US immigrants, after slashing the country's annual refugee intake by more than 50 percent, tightening visa issuance around the world and attempting to ban travellers from 11 countries, most of them with Muslim-majority populations. Uzbekistan is not among the 11.
The programme Trump threatened aims to diversify the origins of people granted permanent residence -- so-called green cards -- in the US.
In 2015, green card lottery applications were received for more than 14 million people, and 49,377 won green cards. That included 2,524 Uzbeks.
Trump said that he wants to move US immigration to a “merit-based system” and not allow immigrants to bring their extended families.
“We want to get rid of chain migration,” he said.