National Economic Council Director Larry Kudlow said Thursday that senators facing scrutiny for moving stock in the run-up to the coronavirus crisis should be "significantly punished" if they are proven to have broken insider trading laws, in comments that departed in tone from President Trump's assessment.

Sens. Dianne Feinstein, D-Calif., Kelly Loeffler, R-Ga., Richard Burr, R-N.C. and Jim Inhofe, R-Okla., have all been reported in recent weeks to have sold large amounts of stock before the market crashed due to concerns about the coronavirus pandemic. The allegations against the senators are all separate, and each has denied any wrongdoing. Several have also either denied access to inside information, or stressed that third parties were making the trades without their input.

Kudlow, however, said on a tele-town hall hosted by Sen. Martha McSally, R-Ariz., that if any of them are found guilty, the justice system should come down hard on them. The comments, first reported by The Hill, were recorded and published on YouTube by the liberal super PAC American Bridge 21st Century.

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"I sure don't, I sure don't, ma'am," Kudlow said in response to a McSally constituent who asked if they thought what the senators accused of insider trading were doing was OK. "If it is proven that they've done something illegal or unethical, they will have to be significantly punished. I don't put up with any of that nonsense."

"Our great system of free enterprise, you know, you've got to play by the rules. By the way, everybody has to play by the rules" Kudlow continued, before going through his lengthy resume that encompasses Wall Street, television and the White House. "We all have to play by the rules and if not we'll have to face the consequences."

McSally responded: "Larry, I couldn't agree with you more. If these allegations are true they need to be held accountable. This is why people are so disgusted with the elite, so if they're true they must be held accountable."

Kudlow's tough talk struck a different tone than Trump's did when he was asked about the allegations in the immediate aftermath of the first reports about the senators' transactions.

"I know everyone mentioned, Dianne Feinstein, I guess and a couple of others. I don't know too much about what it's about but I find them to all be very honorable people," Trump said in a White House coronavirus task force briefing last month. "They said they did nothing wrong. I find them, the whole group, very honorable people."

When pressed on the topic, Trump would not say the senators should be subject to an investigation.

"I don't know because I'd have to look at it. Possibly," Trump said.

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Burr has already called for a Senate Ethics Committee investigation into himself, aiming for "full transparency." He has said his stuck dump, which was valued at between $628,000 and $1.72 million, according to ProPublica, was based only on reports that were public.

Loeffler, who is far wealthier than Burr and unloaded $3.1 million worth of stock, has said that she doesn't make her own investment decisions and this week announced that she had liquidated all of her stock holdings.

Inhofe has also said he is not involved in his investment decisions and Feinstein said the transactions she is accused of were made by her husband and she had no involvement in them.

Fox News' Brooke Singman, Adam Shaw and Dom Calicchio contributed to this report.