Asked whether it's appropriate for President Trump to suggest China investigate the Biden family, Sen. Ted Cruz (R-Texas) told CBS' Margaret Brennan: "Of course not. Elections in the U.S. should be decided by Americans, and it's not the business of foreign countries, any foreign countries, to be interfering in our elections."

BRENNAN: China is a surveillance state. Is it appropriate for President Trump to be saying China should look into the Biden family?

CRUZ: Of course not. Elections in the U.S. should be decided by Americans, and it's not the business of foreign countries, any foreign countries, to be interfering in our elections.

BRENNAN: Even Ukraine? When you're talking about some of this, do you think that, say the president's personal attorney Rudy Giuliani who's been talking about China, who's been talking about Ukraine, do you want to hear him testify about this sort of shadow foreign policy?

CRUZ: Listen, foreign countries should stay out of American elections. That's true for Russia, that's true for Ukraine, that's true for China, that's true for all of them. It should be the American people deciding elections. I don't know what Rudy's been saying. I do know though that we should decide our elections. It should be the American people making those decisions.

The big picture: Trump said on the South Lawn of the White House earlier this month that China should investigate Biden and his son, Hunter, over unsubstantiated corruption allegations, leaving Republicans scrambling over how to respond. While some have called the request inappropriate, others have suggested it was a joke — despite no indication from the White House that it was.

Trump made a similar request of the Ukrainian government, which led to Democrats launching a formal impeachment inquiry.

Cruz said he believes that Giuliani, who has helped lead the campaign to push Ukraine to investigate the Bidens, should accept Senate Judiciary Chairman Lindsey Graham's (R-S.C.) invitation to testify before the committee.

Asked whether the Justice Department should investigate the Bidens, Cruz said he believes they should if there's "credible evidence of a violation of law."

He also added that the Trump administration should release the transcripts of Joe Biden's conversations with Ukraine while he was vice president, much like the White House released a summary of Trump's call with Ukraine's president.

"Use the same standards and let the American people read the transcripts and decide," Cruz said.

Between the lines: Cruz and Trump have a complex relationship. While the 2016 GOP runner-up famously refused to endorse Trump at the Republican National Convention for attacking his family, Cruz has overall been a consistent Trump ally and defender throughout Trump's presidency.

Go deeper: What matters most in the Trump-Ukraine scandal