Presidential candidates condemn Brussels attacks

U.S. presidential candidates rushed Tuesday morning to condemn the deadly attacks in Brussels in which at least 34 people were killed in two separate bombings.

READ MORE: #JeSuisBruxelles trends in wake of Brussels bombings to show support for victims of attack

Calling into several morning news shows, GOP front-runner Donald Trump reiterated his proposal to crack down on those who are allowed to enter the U.S.

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"I would close up our borders to people until we figure out what's going on," Trump said by phone on Fox News Tuesday morning. "We have to be very, very vigilant with who we let into this country."

%shareLinks-quote="I would close up our borders to people until we figure out what's going on​." type="quote" author="Donald Trump" authordesc="GOP Front-Runner" isquoteoftheday="false"%

"We are taking in people without real documentation. We don't know who they are or where they're from. We don't learn," he continued. "I will tell you I've been talking about this for a long time. This whole thing will get worse as time goes by."

RELATED: Scenes from the deadly attacks in Brussels

In a call to NBC News, Trump advocated for the use of torture on Salah Abdeslam, who is suspected of helping plan and carry out terrorist attacks in Paris in November that left 130 dead. Police arrested Abdeslam during a commando-style raid in Belgium last week; he is believed to be the only surviving participant of the attacks.

Intelligence authorities have not yet affirmatively connected the attacks with Islamic State group or any other terrorist group, but early speculation linked Tuesday's airport and subway attacks to Abdeslam's arrest.

Though Abdeslam is said to be cooperating with authorities, Trump said Tuesday he thinks harsh interrogation methods would be justified to get him to talk.

"I am in the camp that torture works," Trump said. "I am in the camp where you have to get the information."

Democratic front-runner Hillary Clinton, speaking to NBC a few minutes after Trump, repudiated his call for closed borders and advocating the use of torture.

%shareLinks-quote="We've got to stand in solidarity with our European allies as they have stood with us on so many occasions​." type="quote" author="Hillary Clinton" authordesc="Democratic Presidential Hopeful" isquoteoftheday="false"%

"We've got to stand in solidarity with our European allies as they have stood with us on so many occasions," she said, adding that it would be "unrealistic that we're going to completely shut down our borders. That would stop commerce, for example."

"The threat posed by the modern incarnation of terrorism is one that we have to be vigilant against," she said, but "we don't need to resort to torture."

Instead, she called for measures to improve intelligence on those who pass through national borders and better international cooperation.

"We have got to tighten our security: I've talked about a visa system and a passenger name record system," she said.

"This is time to reaffirm our commitment to our allies individually and through NATO," she added, apparently in response to Trump's remarks to the influential Jewish lobbying organization American Israel Public Affairs Committee.

During his speech to the group Monday evening, Trump proposed withdrawing some support from NATO, the North American military collective, saying it cost too much money and that other members should take on more of the alliance's financial burden.

In their statements on the Brussels bombing released early Tuesday, both of Trump's rivals for the Republican nomination vowed to go on the offensive against perpetrators of terror.

%shareLinks-quote="Make no mistake -- these terror attacks are not isolated incidents." type="quote" author="Sen. Ted Cruz" authordesc="GOP Presidential Candidate" isquoteoftheday="false"%

"Make no mistake -- these terror attacks are not isolated incidents," said Texas Sen. Ted Cruz, Trump's closest competitor. "They are just the latest in a string of coordinated attacks by radical Islamic terrorists perpetrated by those who are waging war against all who do not accept their extreme strain of Islam."

Cruz has repeatedly criticized President Barack Obama for his refusal to lay blame for the spread of the Islamic State group on "radical Islamic terrorism," as the president seeks to avoid painting all Muslims with the same brush.

"Radical Islam is at war with us. For over seven years we have had a president who refuses to acknowledge this reality," Cruz said. "The truth is, we can never hope to defeat this evil so long as we refuse to even name it."

"That ends on January 20, 2017, when I am sworn in as president," he continued. "We will name our enemy -- radical Islamic terrorism. And we will defeat it."

Ohio Gov. John Kasich said in a statement he was "sickened" by the news and images coming out of Brussels.

%shareLinks-quote="The wave of terror that has been unleashed in Europe and elsewhere around the world are attacks against our very way of life and against the democratic values upon which our political systems have been built." type="quote" author="John Kasich" authordesc="GOP Presidential Candidate" isquoteoftheday="false"%

"We and our allies must rededicate ourselves to these values of freedom and human rights," he continued. "We must also redouble our efforts with our allies to identify, root out and destroy the perpetrators of such evil."

Clinton's rival for the Democratic nomination, Vermont Sen. Bernie Sanders, released this statement later this morning:

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