Ted Cruz Rafael (Ted) Edward CruzSenate Republicans face tough decision on replacing Ginsburg Cruz: Trump should nominate a Supreme Court justice next week Renewed focus on Trump's Supreme Court list after Ginsburg's death MORE pledged to continue an investigation into Hillary Clinton Hillary Diane Rodham ClintonWhat Senate Republicans have said about election-year Supreme Court vacancies Bipartisan praise pours in after Ginsburg's death Trump carries on with rally, unaware of Ginsburg's death MORE's use of a private email server while secretary of State if he is elected president.

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Appearing during an Orlando rally that also served as an interview to air on Fox News's "Hannity," host Sean Hannity asked Cruz if he'd continue to go after Clinton.

"Let's say that the FBI makes a criminal referral to the Justice Department and it is ignored. And you become president, the statute of limitations had not passed — would you aggressively go after Hillary Clinton if the FBI believes she committed felonies?" Hannity said.

"Absolutely yes, and there is a principle here that matters," Cruz said.

"This country was founded on the principle that no one is above the law, and whether it is the Clintons or whether it is some in the Republican Party who think they are above the law, that the law doesn't apply to them, that's not how it works."

Investigations surrouding Clinton are major talking points on the GOP trail as candidates argue that her decision to use a private email server, found to contain emails subsequently marked as classified, should bar her from office.

Clinton pushed back at allegations of impropriety during Wednesday night's debate and swatted down the possibility of an indictment.