On the day when they were locked in battle in the Arizona and Utah primaries, Republican presidential rivals Donald Trump and Ted Cruz actually sounded as if they were partners in the war against terrorism.

Both candidates issued controversial calls on how to fight radical Islamic terrorists just moments after the attacks in Brussels, Belgium that killed at least 34 people and wounded 230 others.

For their hard-hitting anti-terrorism plans, the two quickly found themselves under attack by liberals and even their own party mates.

In an interview with CNN's Wolf Blitzer, Trump once again called for the use of waterboarding as a "minimal form of torture" to get information from suspected terrorists.

He said Belgian authorities could have thwarted Tuesday's terrorist attack in Brussels if they had tortured Salah Abdeslam, the suspected terrorist who was captured days earlier, into spilling out his group's terrorist plans.

Trump said Abdeslam would have talked "a lot faster with the torture."

The Republican presidential frontrunner said he would authorise waterboarding and "far worse" forms of torture against suspected terrorists as president after first broadening existing laws banning torture.

Trump also called for surveillance of radical Islam's tentacles in the U.S., telling talk-radio host Michael Savage there's "a massive, massive problem with radical Islam, whether we like it or not," WND reported.

"We have to have tremendous surveillance, and that includes the mosques," Trump said. "Whether we like it or don't like it. We have to be intelligent people. You see what's going on. This is worldwide."

He said the world is facing a new type of war, but U.S. President, Barack Obama "won't even use the term 'radical Islam.'"

For his part, Cruz also called for greater police surveillance of Muslim neighborhoods in the U.S., comparing it to police boosting their presence in areas with known gang activity.

"If you have a neighbourhood where there's a high level of gang activity, the way to prevent it is you increase the law enforcement presence there and you target the gang members to get them off the streets," the Texas senator told CNN's Anderson Cooper. "I'm talking about any area where there is a higher incidence of radical Islamic terrorism."

Trump said he agreed with Cruz's proposal to target Muslim neighbourhoods, calling it "a good idea."

Cruz's call was quickly denounced by Ohio Gov. John Kasich, the third Republican presidential candidate still in the race. "We are not at war with Islam, we are at war with radical Islam," Kasich said during a news conference. "Just because you happen to be a Muslim does not mean you want to destroy someone in the West."

Democratic National Committee Chairwoman Debbie Wasserman Schultz issued an even harsher rebuttal. "Ted Cruz is a disgrace," the Florida congresswoman said, adding that the freshman senator's statement amounted to "fear-mongering."

Both Trump and Cruz slammed President Obama and his policies, including the U.S. Visa Waiver Program, Fox News reported.

Trump called for an end to the visa programme, which allows roughly 20 million people a year to visit the United States.

"I've been talking about this for a long time, and look at Brussels," Trump said on "Fox & Friends." "Brussels was a beautiful city, a beautiful place with zero crime, and now it's a disaster city."

At a press conference earlier in the day in Washington, D.C., Cruz said the visa waiver programme "no doubt" needs "serious scrutiny."

"Our vetting programs are woefully insufficient," Cruz said, arguing that ISIS has already stated its intentions to try to infiltrate terrorists among the refugees so they can "commit acts of jihad."

"Today's attacks in Belgium underscores that this is a war. This is not an isolated incident. This is not a lone wolf. ISIS had declared jihad. ... The time for the president's political correctness has passed. ... We absolutely have to revisit our immigration policy across the board to prevent Islamic terrorists from coming in," Cruz said.