Ted Cruz. Fox News/screenshot Texas Sen. Ted Cruz kept attacking his rival Donald Trump after they faced off onstage at CNN's Republican presidential debate on Thursday night.

In an extended interview on Fox News, Cruz went after the Republican frontrunner.

"I think that what became very clear is that Donald Trump is not the right candidate to go head-to-head with Hillary Clinton in November," Cruz said. "That on policy issue after policy issue, his position is identical to Hillary."

Cruz cast Trump's policies as in line with those of "liberal Democrats." Trump has previously called himself a Democrat before running for the Republican presidential nomination.

During the same Fox interview, Cruz then hit Trump with a flurry of additional attacks:

"Donald can't defend his own record. Whenever you point out what he's actually said, he just screams, 'liar,' he insults you, he attacks you, he makes it personal. And he gets very rattled. He doesn't like anyone pointing to his actual, substantive record. And I think that's a sign of weakness."

"Whenever you mention his poll numbers, Donald loses it. And in particular, I pointed out that in the last 10 national polls, Donald loses to Hillary in eight of them. And in the last 10 national polls, I either tie or beat Hillary in eight of them. He gets very, very upset."

"It was stunning tonight, ... he ran away from his healthcare plan. For 20 years, Donald has advocated socialized medicine, the government in charge of everyone's healthcare. He said it in the past debates. Tonight he ran away from it, wasn't willing to defend it. It really was striking."

"This is a man who is not prepared to be president and whose views are much, much closer to Hillary Clinton's than they are to Republican primary voters."

"Donald is an entertainer and sometimes he seems to live in his own reality that whatever he says in the moment is the only truth that exists and whatever else he may have said for years in the past doesn't matter."

"While I was leading the fight against amnesty, Donald was firing Dennis Rodman on 'Celebrity Apprentice.' And indeed he was tweeting out, just three years ago, his support for amnesty."

"Donald's own personal record on immigration is terrible. He had a million-dollar court judgment against him for being part of a conspiracy to hire illegal immigrants to build Trump Tower. Just today in the news, it was reported that his hotel down in Florida brings in hundreds of foreign workers instead of hiring American workers."

When asked if his new strategy was going after the frontrunner, Cruz said he's been taken on Trump "for many weeks and months."

Florida Sen. Marco Rubio has also started piling on Trump.

At the debate Thursday night, Rubio and Cruz each went on the attack, hitting Trump on several issues including taxes, immigration, Trump's history as a reality-television host, and his business career. Trump fought back hard, and the real-estate mogul has repeatedly called Cruz a liar:

The repeated clashing came as both Cruz and Rubio are staring far up at Trump in the race for the Republican nomination. Trump is the clear frontrunner in the primary contests, having won the New Hampshire and South Carolina primaries and Tuesday's Nevada caucuses. Rubio and Cruz are both fighting to take Trump down and establish himself as the clear alternative.

Watch Cruz's Fox News interview below: