Story highlights "One person I think would be very, very strong is John Bolton," Cruz told CNN

The comment comes as Trump's national security council is facing turmoil

Washington (CNN) Texas Sen. Ted Cruz is urging President Donald Trump to name John Bolton as his national security adviser, a move that would win conservative support but would anger other Republicans over the former United Nations ambassador's role during the Iraq War.

"One person I think would be very, very strong is John Bolton," Cruz told CNN. "He's someone who understands the world, he understands the threats of radical Islamic terrorism."

The comment comes as Trump's national security council is facing turmoil following the sudden forced resignation of Michael Flynn and the decision by retired Vice Adm. Bob Harward to turn down the job.

But picking George W. Bush's UN ambassador could prompt an uproar in some quarters of the GOP -- especially among libertarian-leaning senators like Rand Paul of Kentucky, who furiously opposed the possibility of naming Bolton to the State Department. Paul has been sharply critical of Bolton's worldview, especially his strong support of the Iraq War -- a war Trump himself said on the campaign trail he strongly opposed.

"When it comes to foreign policy, Rand and I do not see eye-to-eye," Cruz told CNN. "I share Rand's concern that we should not be overeager to engage in military conflict. That's exactly right and I actually think... John Bolton agrees with that proposition as well."

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