Democratic presidential front-runner Hillary ClintonHillary Diane Rodham ClintonGeorge HW Bush wears 'book socks' to Barbara Bush's funeral to honor her passion for literacy Obamas, Clintons to attend funeral of Barbara Bush Hillary Clinton to fundraise in DC for public charter high school MORE is pushing back on Donald TrumpDonald John TrumpFlynn to campaign for Montana GOP Senate candidate Trump considering pardon for boxing legend after call from Sylvester Stallone Decline in EPA enforcement won't keep climate bill from coming MORE's claim that he could close the nation's borders after a terrorist attack, remarks that follow a series of bombings Tuesday in Brussels.

"It's unrealistic to say that we're going to completely shut down our borders to everyone," Clinton said during an interview on NBC's "Today" show.

Trump, the Republican presidential front-runner, earlier Tuesday said if he was president he would have closed the nation's borders in the wake of coordinated terrorist attacks in Belgium that left more than 34 people dead and scores injured.

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"I would close up our borders to people until we figure out what is going on," Trump said during a phone interview on "Fox and Friends."

Trump appeared to dial back his comments later, telling "CBS This Morning," "I didn't say shut it down."

"I said you have to be very careful. We have to be very, very strong and vigilant at the borders. We have to be tough," Trump added.

Clinton on Tuesday invoked her experience as secretary of State, saying that in her dealings with Europeans they were often "reluctant" to employ tougher security measures. But she argued they were necessary to prevent future attacks.

"We have been confronting the threat of terrorism for quite some time and with the latest terrible manifestation of it, we've got to tighten our security," Clinton said. "I've talked about a visa system and a passenger name record system."

Clinton also encouraged support for NATO a day after Trump suggested the U.S. reduce funding for the organization and rethink its involvement. 

Ted CruzRafael (Ted) Edward CruzCruz's Dem challenger slams Time piece praising Trump Race for Republican Speaker rare chance to unify party for election 32 male senators back Senate women's calls to change harassment rules MORE, Trump's main rival for the Republican nomination, also ripped the GOP front-runner for his comments on NATO a day before the attacks in Brussels.

"Donald Trump is wrong that America should withdraw from the world and abandon our allies," Cruz told reporters in Washington. 

This story was updated at 10:12 a.m.