Washington (CNN) President Donald Trump , during a White House Cabinet meeting Wednesday, said he wants to terminate the Diversity Visa Lottery, a program that distributes around 50,000 visas to countries where there is a low rate of immigration to the US.

"I am, today, starting the process of terminating the diversity lottery program," Trump said, seated next to Secretary of State Rex Tillerson and Defense Secretary Jim Mattis. "I am going to ask Congress to immediately initiate work to get rid of this program, diversity lottery, diversity lottery. Sounds nice, it is not nice, it is not good. It hasn't been good and we have been against it."

He added: "We're going to quickly as possible get rid of chain migration and move to a merit-based system."

Trump added that based on preliminary information, the attacker in New York "was the point of contact, the primary point of contact for, and this is preliminarily, 23 people, that came in or potentially came in with him and that is not acceptable."

Four people on the school bus had minor injuries after the truck crashed into it, a police official said. After hitting the bus, the driver exited the truck and was shot by police while displaying imitation firearms, according to the NYPD.

Four people on the school bus had minor injuries after the truck crashed into it, a police official said. After hitting the bus, the driver exited the truck and was shot by police while displaying imitation firearms, according to the NYPD.

The driver of the truck drove the wrong way down the West Side Highway bike path for several blocks, according to two senior law enforcement sources at the New York Police Department. After striking multiple people, the driver hit a school bus and wrecked the truck, an NYPD official said.

The driver of the truck drove the wrong way down the West Side Highway bike path for several blocks, according to two senior law enforcement sources at the New York Police Department. After striking multiple people, the driver hit a school bus and wrecked the truck, an NYPD official said.

New York City police work in Manhattan after a rental truck drove down a busy bicycle path and struck people on Tuesday, October 31. At least eight people were killed in the incident, which is being investigated as terrorism, according to multiple law enforcement sources. A suspect is in custody.

New York City police work in Manhattan after a rental truck drove down a busy bicycle path and struck people on Tuesday, October 31. At least eight people were killed in the incident, which is being investigated as terrorism, according to multiple law enforcement sources. A suspect is in custody.

The comments follow Trump's tweets on Wednesday morning that blamed Sen. Chuck Schumer, a New York Democrat, for the program.

"The terrorist came into our country through what is called the 'Diversity Visa Lottery Program,' a Chuck Schumer beauty," Trump tweeted. "I want merit based."

Schumer was a key shaper of the 1990 legislation that created the program, but also played a lead part in the 2013 Gang of Eight bill that that passed the Senate on a bipartisan basis and included removing the diversity lottery program. The bill would have moved those visas elsewhere in the system and introduced a merit system that took into account multiple factors like family and work skills.

The diversity visa has been a point of contention for years. The 50,000 visas, distributed by random selection among countries where there is a low rate of immigration to the US, were originally designed to diversify the pool of immigrants to the US. The visas offer immigrants green cards, permanent legal residence and a path to citizenship.

Republican Sens. Tom Cotton and David Perdue have introduced a bill, endorsed by Trump, that would eliminate the diversity lottery and certain categories of family-based green cards, and then would transform the remaining employment-based visas into a point system that favors heavily highly skilled, highly educated, English-speaking immigrants.

But while there is consensus around needing to reform the process, limited support exists even within the GOP for Cotton and Perdue's bill.

Sen. Jeff Flake, an Arizona Republican who has been an ardent critic of Trump, noted in a tweet Wednesday that the Gang of Eight bill, had it been signed into law, would have done away with the diversity visa program.

The Cotton-Perdue bill would roughly halve the number of green cards overall per year, a point of contention for many Democrats and Republicans alike, and wouldn't easily allow for low skilled immigrants to come to the US permanently, another sticking point for many.

Initial response

Trump also labeled the alleged attacker an "animal" to reporters Wednesday, and said the United States must "get much tougher" with terror suspects.

Trump called for "quick justice" and "strong justice" for terror suspects.

"What we have right now is a joke and it is a laughing stock and no wonder so much of this stuff takes place," Trump said.

The President's initial Twitter response to the attack labeled the attacker a "very sick and deranged person" and offered his "thoughts, condolences and prayers to the victims and families of the New York City terrorist attack."

Trump later tweeted that he was ordering his Department of Homeland Security to "step up our already Extreme Vetting Program."

It was not clear what program the President was referring to. Reached Tuesday night, DHS referred all questions on the "vetting" order to the White House, which did not respond to questions.

Soon after Trump tweeted Wednesday morning, Schumer responded with a tweet of his own: "I guess it's not too soon to politicize a tragedy."

Schumer also accused the President of "politicizing and dividing America" and urged him to focus "on the real solution -- anti-terrorism funding -- which he proposed cutting in his most recent budget."

New York Gov. Andrew Cuomo, a Democrat, said at a Wednesday morning news conference that the President's tweets were "not helpful."

"I don't think they were factual. I think they tend to point fingers and politicize the situation," he said. "You play into the hands of the terrorist to the extent that you disrupt, divide and frighten people in the society. The tone now should be the opposite -- on all levels."

Trump's decision to address immigration policy hours after the terrorist attack is markedly different than the tack the White House took after a shooter in Las Vegas opened fire on a concert last month, killing 58.

White House press secretary Sarah Sanders, asked about gun control policy the day after the shooting in Las Vegas, dismissed the idea of talking about policy so soon after a shooting.

"We haven't had the moment to have a deep dive on the policy part of that," Sanders said. "We've been focused on the fact that we had a severe tragedy in our country. And this is a day of mourning, a time of bringing our country together, and that's been the focus of the administration this morning."

Pressed on why Trump brought up the travel ban hours after shootings in Orlando and San Bernardino, Sanders added at the time, "I think there's a difference between being a candidate and being the President."

Right-wing sites blame Schumer

JUST WATCHED Flake slams Trump's tweets, defends Schumer Replay More Videos ... MUST WATCH Flake slams Trump's tweets, defends Schumer 01:04

Tuesday's terror attack in New York was the city's deadliest since 9/11. Sayfullo Habibullaevic Saipov drove a rented van down a bike path, law enforcement sources have said. The attack killed six victims instantly, while two others died later. New York politicians and officials quickly labeled the incident a terror attack.

Right-wing blogs and publications began blaming Schumer's immigration policies on Tuesday night and Trump's comments track with much of what was written.

"Blame Democrat Senator Chuck Schumer," read a post from the Gateway Pundit.

Breitbart, the right-wing publication run by Steve Bannon, Trump's former chief strategist, was leading with a story about the Diversity Visa Lottery Program, citing an ABC New York story that reported Saipov came to the United States through the program.

Turning to immigration politics shortly after a terrorist attack has become a pattern for Trump.

After a deadly mass shooting in San Bernardino, California, in 2015, then candidate-Trump called for the "total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what is going on."

Trump ran on hard-line immigration policies in 2016, pledging to build a wall along the US-Mexico border, cut down the number of refugees coming into the United States and deporting undocumented immigrants currently in the United States.

After stepping into the Oval Office in January, Trump proposed a sweeping travel ban that banned immigration from a series of countries. The ban, which has been repeatedly altered and fought in court, currently puts increased screening on nationals from Chad, Iran, Libya, Somalia, Venezuela and Yemen. Immigration from North Korea and Syria is suspended entirely.

Democrats slammed Trump on Wednesday for quickly turning to immigration after the terror attack.

"This has become the pattern for President Trump, dating back to the campaign," Rep. Adam Schiff, D-California, told MSNBC. "No matter where an attack happens around the world, whether it's in the United States, Europe, he immediately goes to questions about immigration."