Republican presidential candidate Jeb Bush on Friday denounced a plan by rival Donald TrumpDonald John TrumpTrump pushes back on recent polling data, says internal numbers are 'strongest we've had so far' Illinois state lawmaker apologizes for photos depicting mock assassination of Trump Scaramucci assembling team of former Cabinet members to speak out against Trump MORE to establish IDs and a database to track Muslims in the United States.

Bush brought up the issue during an interview on CNBC when a host questioned whether more extreme actions may resonate with the public, such as Japanese internment under Franklin D. Roosevelt.

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"You talk about internment, you talk about closing mosques, you talk about registering people — that's just wrong," the former Florida governor said on the program.

"It's not a question of toughness. It's manipulating people's angst and their fears. That's not strength; that's weakness," Bush added.

Trump doubled down Thursday night when asked by NBC News if he would establish a database to track Muslims, something he refused to rule out earlier this week.

“I would certainly implement that, absolutely,” the celebrity businessman told the news outlet after a campaign event in Iowa. Trump said he would get people into the system through "good management" and use it to keep people from immigrating to the U.S. illegally. He's also said he would close mosques.

"There should be a lot of systems, beyond databases," Trump said.

Trump and several other GOP candidates, such as Sen. Ted Cruz (R-Texas), have strongly opposed President Obama's plan to admit 10,000 Syrian refugees to the U.S. over the next year.

Bush has urged caution on accepting the refugees, balancing a desire to accept those fleeing violence with a need to vet them properly amid fears terrorists might slip in with them.

"There are things that are important as it relates to the values that we have as a country that make us special and unique ... and we will never abandon them in the pursuit of this fight," Bush said Friday.

"On the left, we have Barack Obama who is constantly saying that anybody who disagrees is bad or he ascribes bad motives. And on the right we have an emerging group as well that would tell us that we should abandon American values," Bush said on CNBC. "I think we need to be resolute in the fight against Islamic terrorism. Call it what it is, create a strategy, deal with it."