President-elect Donald Trump plans to act on the "first day" of his presidency on the cases of some Jan. 6 defendants and said he believes the House members on the select Jan. 6 committee who investigated the 2021 Capitol riot, including Democratic Rep. Bennie Thompson and former GOP Rep. Liz Cheney, "should go to jail."

In an interview that aired Sunday on NBC News' "Meet the Press," Trump told host Kristen Welker he would not direct the FBI director or attorney general to do so, but said "I think they'll have to look at that."

The president-elect was also pressed on whether he would pardon some or all of the Capitol riot defendants. He indicated he would not issue a universal blanket pardon: "We're going to look at independent cases." Last week, one of Trump's Senate allies, GOP Sen. Eric Schmitt of Missouri, told CBS News he thinks Trump and the next attorney general should be going through the riot defendants on a "case-by-case" basis.

Trump said of the Jan. 6 defendants and convicts, "I'm going to be acting very quickly," adding that he planned to act as soon as he's inaugurated in January. "First day," he said.

CBS News' review of Justice Department filings shows there have been approximately 1,560 Jan. 6 defendants, and approximately 590 of them are charged with assaulting police. More than 900 defendants have pleaded guilty.

Several of the defendants have openly predicted pardons from Trump are imminent — including for those accused of violent acts.

Over the weekend, Joseph Hutchinson, who is accused of beating police during the Capitol riot and was a fugitive from justice for three years as he eluded authorities, said in a filing that he wants to be released immediately, arguing, "No one is going to flee from a trial that isn't coming. I will await my pardon like any responsible person."

Trump has not yet said if he'll allow new Capitol riot prosecutions, investigations or pending prosecutions to continue. Hundreds more arrests have been expected.

The president-elect was also asked by Welker if he intended to appoint "a real special prosecutor to go after the most corrupt president in the history of the United States, Joe Biden and the entire crime family," as he said he would last year on Truth Social.

"No, I'm not doing that unless I find something that I think is reasonable," Trump said. "But that's not going to be my decision." He said he would leave it up to Pam Bondi, who he intends to name attorney general and Kash Patel, his pick for FBI director.

He said he would leave it to Bondi to determine whether to investigate special counsel Jack Smith, who brought both federal criminal cases against Trump, one on election interference in 2020 and another on documents he allegedly took after his first term from the White House to his Florida residence.

"I want her to do what she wants to do," he said of investigating Smith, whom he referred to as "corrupt." "I'm not going to instruct her to do it."