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Republican presidential candidate Sen. Ted Cruz, R-Texas, addresses the bombings in Brussels during remarks March 22, 2016 in Washington, D.C. Reports indicate at least 30 people have died and scores more injured in the bombings at the airport and metro. Win McNamee/Getty Images

After Tuesday’s terrorist attacks in Brussels that left at least 30 people dead, American presidential candidates were quick to offer condemnation and prescriptions to prevent future attacks, bringing the debate over Muslim immigration in the United States back to the forefront.

Leading Republican presidential candidate Donald Trump called in during “Fox & Friends” Tuesday morning to double down on his idea of temporarily banning Muslims from entering the U.S., a policy he first proposed in December after the Paris attacks.

“I would close up our borders to people until we figure out what’s going on,” Trump said on the phone. “We have to be very, very vigilant with who we let into this country. We are taking in people without real documentation. We don’t know who they are or where they’re from.”

Trump painted a dire picture, adding: “This is going to get worse and worse.”

Trump later appeared on ABC’s “Good Morning America” to reiterate that he would be bring back the practice of waterboarding terrorism suspects if he were to take office.

“And I would try to expand the laws to go beyond waterboarding,” he said.

Ohio Gov. John Kasich issued a statement saying the United States “must redouble our efforts with our allies to identify, root out and destroy the perpetrators of such acts of evil.” He also called in to MSNBC, where he described Islam as a peaceful religion but added that Syrian immigration should be halted temporarily.

“I've asked for a pause in the number of Syrian refugees coming in,” said Kasich, adding that there is a need for a better vetting process.

Kasich also called in to Fox Business News, saying President Barack Obama should abandon his Cuba trip in the wake of the attacks. "He should come home and begin to coordinate with our friends and heads of states around the world and dispatching teams of people to figure out exactly why we have these vulnerabilities."

Texas Sen. Ted Cruz posted a statement to Facebook excoriating Obama’s language when discussing terrorism and calling for scrutiny of both Muslim immigration to the U.S. and of those Muslims who are already here.

“Radical Islam is at war with us. For over seven years we have had a president who refuses to acknowledge this reality. And the truth is, we can never hope to defeat this evil so long as we refuse to even name it,” Cruz said. “That ends on Jan. 20, 2017, when I am sworn in as president. We will name our enemy — radical Islamic terrorism. And we will defeat it.”

Cruz echoed Trump's sentiments about Muslims, as well. "We need to immediately halt the flow of refugees from countries with a significant al Qaeda or ISIS presence," Cruz said. ISIS is another name for the Islamic State terrorist group, which claimed responsibility for Tuesday's attacks in Brussels.

But Cruz also emphasized monitoring the Muslims already in the United States. "We need to empower law enforcement to patrol and secure Muslim neighborhoods before they become radicalized," he said.

When meeting with reporters Wednesday morning, Cruz continued to focus on immigration.

“The attack in Brussels is in many ways the fruit of a failed immigration policy in Europe that has allowed a massive influx of radical Islamic terrorists into Europe,” Cruz said. “Europe is in the process of allowing policies to fundamentally threaten the safety and security of its citizens. That is a mistake.”

Cruz added that the United States Visa Waiver Program, which doesn’t require visas from visitors of 38 countries who are staying in the U.S. for less than 90 days, needs “serious scrutiny.”

Even Democratic front-runner Hillary Clinton said the United States has to “tighten our security” when she called in to the "Today" show Tuesday, adding that she has several proposals for stronger visa requirements, as well as “a passenger name record system.”

But the former secretary of state of scoffed at the idea of shutting down all immigration.

"It's unrealistic to say we're going to completely shut down our borders,” Clinton said. “That would stop commerce, for example.”

Sen. Bernie Sanders of Vermont also issued a statement late Tuesday morning, offering “deepest condolences to the families who lost loved ones ... Today’s attack is a brutal reminder that the international community must come together to destroy ISIS. This type of barbarism cannot be allowed to continue.”