As Donald Trump and Hillary Clinton fought to extend their delegate leads over underdog presidential rivals Tuesday's western U.S. contests, all candidates grappled with a new wave of bloody attacks in Europe.

The contests in Arizona, Utah and Idaho were largely an afterthought for much of the day as the leading White House hopefuls clashed over how to stop the spread of ISIS. The organization claimed responsibility for a series of attacks in Brussels that left at least 31 dead and dozens more wounded.

Even before Tuesday's violence, foreign policy had emerged as a central theme ahead of the western elections with candidates in both parties courting pro-Israel activists this week.

Clinton as well as Trump's Republican rivals questioned whether the billionaire businessman has the temperament and readiness to serve as commander-in-chief, and condemned the Republican front-runner's calls to diminish U.S. involvement with NATO.

Republican calls 'dangerous,' Clinton says

Trump vowed to defeat ISIS, and he renewed his proposal for temporarily barring Muslims from entering the country in addition to refusing entry to Syrian refugees fleeing their war-torn nation.

The GOP front-runner also intensified his past calls for the U.S. to engage in harsher interrogation techniques, arguing that Belgium could have prevented the bombings had it tortured Salah Abdeslam, a suspect in last year's Paris attacks who was arrested last week.

Rep. Adam Schiff of California, the top Democrat on the House Intelligence Committee, said earlier Tuesday the Brussels plot was probably already underway before the suspect's arrest and that his apprehension may have sped up its execution.

When reminded that international law prohibits torture, Trump responded: "Well, I would say that the eggheads that came up with this international law should turn on their television and watch CNN right now, because I'm looking at scenes on CNN right now as I'm speaking to you that are absolutely atrocious."

Clinton took aim at the two top Republican candidates in her speech late Tuesday in Seattle after she was projected as the Arizona primary winner.

"In the face of terror ... We can't throw out everything we know about what works and what doesn't and start torturing people," said Clinton, to a mixed reaction from the crowd. "What Donald Trump, Ted Cruz and others are suggesting is not only wrong, it's dangerous."

Trump was undeterred, telling Britain's ITV television early Wednesday that Muslims were failing to report suspicious activity and they must do more to help prevent attacks such as the ones in Belgium.

"When they see trouble they have to report it, they are not reporting it, they are absolutely not reporting it and that's a big problem," Trump said.

Cruz wants to 'secure' Muslim neighbourhoods

Cruz seized on Trump's foreign policy inexperience while declaring that the U.S. is at war with ISIS.

GOP 2015 Cruz Belgium Attacks

Ted Cruz's comments about surveillance were condemned by New York Police Commissioner William Bratton and the The Council on American-Islamic Relations, among others. (Jacquelyn Martin/The Associated Press)

Cruz said in the wake of the attacks that surveillance in Muslim neighbourhoods in the U.S. must be intensified. He said the U.S. should stop the flow of refugees from countries where the Islamic State militant group has a significant presence.

"We need to empower law enforcement to patrol and secure Muslim neighbourhoods before they become radicalized," the Texas senator said in a statement.

New York Police Department Commissioner William Bratton objected to Cruz's remarks Tuesday, saying: "I take great offense at his characterization of that whole population. ... He's really out of line."

The Council on American-Islamic Relations, the nation's largest Muslim civil rights and advocacy organization, condemned the calls for surveillance, saying it sends "an alarming message to American Muslims who increasingly fear for their future in this nation and to all Americans who value the Constitution and religious liberties."

Republican candidate John Kasich on Tuesday criticized his Republican opponents for targeting Muslims in their responses to the Brussels violence.

Kasich told reporters in Minnesota he doesn't believe all Muslims in Minnesota or elsewhere are "somehow intent on trying to destroy our families." He said, "This is a time when you have to keep your cool."