(CNN) Senate Judiciary Chairman Chuck Grassley on Monday rejected Democratic calls for the committee to bring Donald Trump Jr. back to testify again about the June 2016 Trump Tower meeting following Michael Cohen's claims that Trump Jr. told his father about the meeting in advance.

"If he misled the committee, he's lying to Congress. That's a crime," the Iowa Republican told CNN. "And that'd be up to the prosecutors, not me."

Asked whether he would subpoena Trump Jr. for his phone records — which include calls Trump Jr. placed to a blocked number while setting up the Trump Tower meeting — Grassley said he didn't think there was much more the committee needed to hear from Trump's son.

"I think if he didn't tell us the truth, that that's an issue for the Justice Department, not us," Grassley said. "And I'm not suggesting anything, I'm just saying there wouldn't be much more for us to hear from him."

Last week, CNN reported that Cohen, Trump's former personal lawyer, claims Trump was told ahead of time about the meeting in which Trump Jr. was expecting "dirt" on Hillary Clinton. The claims, if proven true, would contradict the denials from the President and Trump Jr., including the testimony that Trump Jr. gave to the committee last year.

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