"Ted Cruz has changed his positions on ethanol, immigration, H-1B visas. He's changed it on whether marriage is a state or a federal issue. He's changed it on whether he's going to be a real champion for religious liberty or whether that's going to be way down the road and it's not important," Huckabee told CNN's Chris Cuomo on "New Day."
"I think it's pretty clear while Ted Cruz has questioned the integrity of a lot of different candidates on that stage, if you look at how many different things, including trade -- he wrote an op-ed in the Wall Street Journal saying it was the greatest thing since toothpaste, then he came out when the political wind shifted and said he was against it."
According to CNN's "poll of polls" for Iowa earlier this week, Donald Trump is leading Cruz in a tight battle, 31% to 26%.
Huckabee didn't make it onto the main stage for Thursday night's Fox New Republican debate, but instead took part in the earlier "undercard" debate. The Arkansas Republican, who is trailing in the polls, then attended an event to raise money for veterans that was hosted by Donald Trump, who boycotted the debate.
Huckabee, who has repeatedly accused Cruz of offering varying stances on issues to different audiences, said that when a candidate shifts positions so frequently it raises an issue of whether voters can trust that person.
"When people change their views depending on geography of where they happen to be, if they say one thing in Manhattan and another thing in Marshalltown, Iowa, that's when you start wondering whether you can trust them," Huckabee said on "New Day."
"When a person changes views time after time and is always moving with the political wind vane, when a person is a thermometer instead of a thermostat, that person is not a leader and, no, you cannot trust them."
Kentucky Sen. Rand Paul also opened up a similar line of attack on Cruz on Friday, accusing his fellow senator of creating "false narratives."
"I guess the problem with his authenticity is that he is now saying he was never for amnesty," Paul said on Fox News' "Fox and Friends." "I think Ted wants to have it both ways, but he also wants to accuse everybody else of not being as pure as he is, but in reality I think he's creating a false narrative."