Trump had suggested on Wednesday sending Saipov to the Guantanamo Bay military prison in Cuba, where terrorism suspects apprehended overseas are held, but on Thursday he said doing so would be too complicated.
"Statistically that process takes much longer than going through the Federal system", Trump said in an early morning tweet, adding that there is "also something appropriate" about keeping him "in the home of the frightful crime he committed". "There is also something appropriate about keeping him in the home of the frightful crime he committed".
Trump on Wednesday referred to the the US justice system as a "joke" and a "laughing stock".
Tuesday's assault was the deadliest in NY since the September 11, 2001, when more than 2600 people died in the World Trade Centre attack. "Should move fast. DEATH PENALTY!" the president said in a tweet.
The maximum penalty for the first is death; the maximum for the second life in prison, Kim said.
Saipov's defense attorney did not immediately respond to a request for comment.
When it comes to Saipov's case, proving that the President's comments have not harmed the man's chance of a fair trial may come down to the judge ruling that people don't listen to or respect Mr Trump's comments, according to executive editor Elie Mystal.
"I'm not someone who believes in the death penalty in general", New York's Democratic Mayor Bill de Blasio told a news conference on Thursday.
After a gunman shot dead 58 people last month in Las Vegas, IS claimed the killer was also one of its "soldiers" but the Federal Bureau of Investigation said it found no such links with the accused, Stephen Paddock.
There are now 61 people, including one woman, on death row for federal crimes.
Experts say the federal government, unlike some states, shows little eagerness to execute - and in any case, appeal processes can last years and even decades. "I think most Americans right now would say, "Yes, give him the electric chair, give him the gas chamber, give him the needle".
The law enforcement official said Kadirov was a friend of Saipov's and may not have a role in the case at all, but authorities got suspicious because he "went off the radar" when they went to speak with him.
He also called for tougher "merit-based" immigration measures and vowed to do away with the diversity visa programme. The group has often taken credit for the actions of self-radicalized attackers, such as Omar Mateen - the man who killed 49 people at the Pulse nightclub in Orlando in June 2016.
Investigators said Wednesday that the man who mowed down cyclists and pedestrians in NY the day before had confessed to acting in the name of IS and said that he "felt good" about the killings.