President Obama on Wednesday delivered a sharply personal rebuke of GOP presidential candidate 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 for his call to institute surveillance on Muslim communities in response to the Brussels terrorist attacks.

During a press conference in Argentina, Obama called such a proposal “wrong and un-American” and said it would undermine the U.S. campaign against Islamic extremists.

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Obama invoked Cruz’s Cuban heritage, arguing the Texas senator was ignoring the personal journey of his father, who fled the island nation for the United States to escape political oppression.

“I just left a country that engages in that kind of neighborhood surveillance, which, by the way, the father of Sen. Cruz escaped for America,” the president said. “The land of the free. The notion that we would start down that slippery slope makes absolutely no sense.”

It was the second day in a row Obama addressed the series of blasts in the Belgian capital that killed at least 31 people and injured more than 180, including a dozen Americans.

The Brussels attacks shook up the presidential campaign with fresh concerns about the threat of terrorist attacks on U.S. soil.

Some Republican candidates have called for drastic measures to prevent a similar strike in the U.S.

Cruz said Muslim neighborhoods should be put under special watch by authorities in order to preempt any future attacks in the U.S.

GOP presidential front-runner Donald Trump Donald John TrumpObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE backed Cruz on the patrols and renewed his call for a temporary ban on Muslims entering the country and for waterboarding to be used on terrorism suspects.

The proposals touched off a fierce political debate, with Democrats accusing Trump and Cruz of encouraging Islamophobia to win over conservative votes.

Candidates on both sides of the aisle called for tougher security measures in the U.S. and demanded Obama take a more aggressive approach to fighting the Islamic State in Iraq and Syria (ISIS), which claimed responsibility for the attacks.

But Obama indicated he would not make significant changes to his anti-ISIS strategy "simply because it's political season."

The president said defeating the group is his “No. 1 priority,” but it must be done in a “smart” way.

“As our strategy evolves and we see additional opportunities, we will go after it,” Obama said.

But he said the U.S. should not “take approaches that will be counterproductive," such as carpet-bombing Middle Eastern countries, an idea Cruz proposed.

“Not only is that inhumane, not only is that contrary to our values, but that would likely be an extraordinary mechanism for ISIL to recruit more," Obama said, using an alternate acronym for the group. “That’s not a smart strategy.”

The president pledged he would "continue to go after ISIL aggressively until it is removed from Syria and removed from Iraq and is finally destroyed."

The U.S. has relied on airstrikes to fight the extremist group and has mostly turned to local forces on the ground, resisting calls for a large-scale ground campaign.

American special operations forces have carried out strikes against certain ISIS targets, and the Marines recently set up a base in northern Iraq with around 200 troops. One Marine was killed in an ISIS rocket attack there last Saturday.

At the same time, Obama reiterated his belief that the group does not pose "an existential threat" to the U.S. and said that its activities should not disrupt the daily lives of Americans.

"Even as we are systematic and ruthless and focused in going after them ... it is very important for us to not respond with fear," the president said. "We defeat them in part by saying, 'You are not strong. You are weak.' "