Sen. John Cornyn John CornynThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight Senate GOP faces pivotal moment on pick for Supreme Court MORE (R-Texas) on Monday dismissed President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE's question about whether "Saturday Night Live" ("SNL") should be investigated, saying the president's tweets sometimes get him "off message."

"Many of us who are trying to help and work with the president ... have tried to get him to put down his iPhone and his Twitter account. But he thinks that's what helped get him elected, and he likes the idea of communicating directly," Cornyn told a Texas radio station when asked about Trump's suggestion that the late-night comedy show should be probed for its frequent criticism of him.

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"But I think the volume of them and the subject matter sometimes gets him ... well, frequently gets him off message where he'd be better off staying on a more narrow and disciplined message," continued Cornyn, who is up for reelection in 2020.

Cornyn was asked about Trump's tweets from over the weekend in which he criticized "Saturday Night Live" after the sketch comedy show aired a rerun featuring a skit depicting a world in which he had never become president.

"I don't take that seriously, honestly," Cornyn said.

Trump, in a pair of tweets on Sunday morning, complained that "SNL" and other late-night comedy shows "can spend all of their time knocking the same person (me), over & over, without so much of a mention of 'the other side.' Like an advertisement without consequences."

In a separate tweet, Trump asked, "Should Federal Election Commission and/or FCC look into this?"