NEW YORK (CBSNewYork) -- Donald Trump wants to close the borders as Sen. Ted Cruz is calling for law enforcement to patrol Muslim neighborhoods following Tuesday's deadly terror attacks in Brussels.
CBS2's Dick Brennan reported Tuesday that Trump is doubling down on his immigration proposals after more than 30 were killed when bombs went off at a Brussels airport and metro station.
"I would close up our borders to people till we figure out what is going on. I mean, look at Brussels, look at Paris, there are so many cities that are great cities," Trump said.
Trump reversed himself on CBS, saying, "I didn't say, 'Shut down the borders,'" but went back to his earlier comments later on Fox Business, again saying, "We have to close our borders."
The Republican presidential front-runner already called for a ban on Muslims entering the United States, in part out of fears of terrorism.
"We don't know where they are from, who they are. You look at them and from any standpoint they could be ISIS, they could be ISIS related. We just don't learn, we just don't learn," Trump said.
"I would be extremely careful about people from the Middle East coming into our country. I would be extremely careful as to what's going on," Donald Trump told CBS News. "You have an ISIS problem that's a massive problem. They want to come in, they want to do big damage, and I would be extremely careful about that."
Trump said he would "absolutely" question people arriving from the Middle East at airports.
Trump added that waterboarding would be fine if it was up to him.
Trump also advised that the U.S. should scale back its involvement with NATO, which is based in Belgium.
CBS2's Kristine Johnson reported Trump took to Twitter later Tuesday to call out President Barack Obama for attending a baseball game in Cuba.
"Pres. Obama should leave the baseball game in Cuba immediately & get home to Washington- where a #POTUS, under a serious emergency belongs!" Trump tweeted.
For his part, Cruz said the U.S. needs to "immediately halt the flow of refugees from countries with a significant al Qaeda or ISIS presence."
"We need to empower law enforcement to patrol and secure Muslim neighborhoods before they become radicalized. We need to secure the southern border to prevent terrorist infiltration. And we need to execute a coherent campaign to utterly destroy ISIS," Cruz said in a statement.
The Republican presidential hopeful said Obama has not been tough enough on ISIS.
"It is long past time that we had a president who will acknowledge this evil, will call it by its name and utilize the full force and fury of the United States to defeat radical Islamic terrorism to defeat ISIS," the Texas senator said.
Shortly after the deadly attacks, Cruz released a statement, saying "radical Islam is at war with us."
"Our hearts break for the men and women of Brussels this morning. Make no mistake -- these terror attacks are no isolated incidents. They are just the latest in a string of coordinated attacks by radical Islamic terrorists perpetrated those who are waging war against all who do not accept their extreme strain of Islam," Cruz said. "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. That ends on January 20, 2017, when I am sworn in as president. We will name our enemy -- radical Islamic terrorism. And we will defeat it."
Democratic presidential candidate Hillary Clinton said Trump's ideas send the wrong signal to the rest of the world.
"To do anything that implies we are at war with an entire religion, with 1 or 1.2 or 4 billion people is not only wrong, it is dangerous," the former secretary of state said. "You know, right here at home, we need to be reaching out and included Muslim-Americans and communities where they live."
Clinton said the U.S. has to do more with "terrible attacks like this."
"I've been calling for closer cooperation, looking at all of our laws and our rules at what works and what doesn't against such a determined enemy. We have to keep increasing pressure on them in the region and we have to dismantle their network of arms, recruiting and propaganda," she said.
Clinton added, "They are certainly showing they can wage attacks, but remember, the primary goal of terrorists is terrorize, to intimidate, to force people to undermine the democratic values that are our the foundation of our alliance, our way of life. We can't panic in the face of these things. We have to be strong, smart and steady in how we respond."
Ohio Gov. John Kasich released a statement condemning the attacks, saying, "Along with every American, I am sickened by the pictures of the carnage, by the injuries and by the loss of life."
"I want to express my solidarity with the people of Belgium in the aftermath of the attacks that took place in Brussels," said Kasich. "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."
Kasich said that President Barack Obama should have returned back to Washington following the attacks.
"Had I been president, I would have cut short my visit, flown home, conducted calls jointly with heads of state and begun to assemble teams of people, intelligence experts who can take a look at the serious breaches we have in intelligence," he told reporters.
Kasich added that the U.S. "must strengthen our alliances as our way of life and the international system that has been built on our common values since the end of the Second World War comes under challenge from these and other actors of evil."
Former GOP presidential candidate Marco Rubio also spoke on ISIS on his Twitter account, saying: "The US and Europe must be united in striking ISIS wherever they seek safe haven to dismantle this terrorist threat once and for all."
Sen. Bernie Sanders says the U.S. has to step up even more on the war on terror.
"We are making progress in Iraq -- ISIS is losing about 20 percent of the territory they held last year -- but clearly we have got to do more," the Democratic hopeful said.
The Islamic State of Iraq and Syria has taken responsibility for the deadly terror attacks in Brussels. More than 200 people were wounded.
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