WASHINGTON: Republican Donald Trump and Democrat Hillary Clinton held their leads in the battle for their parties' 2016 presidential nomination in the latest state-by-state voting as the Islamic State terrorist organisation inserted itself deeper into American politics with the attacks it claimed in Belgium.

While both front-runners scored victories in the night's biggest prize of Arizona, Democratic challenger Bernie Sanders won caucuses in Utah and Idaho and Republican Ted Cruz claimed his party's caucuses in Utah.

Cruz gained some momentum on Wednesday as former candidate Jeb Bush said he's endorsing the Texas senator for president, tweeting that Cruz is a "consistent, principled conservative who has shown he can unite the party." Bush added on Facebook that Republicans "must overcome the divisiveness and vulgarity Donald Trump has brought into the political arena" or risk losing to Clinton.

But Cruz drew a sharp rebuke from Muslim Americans and civil rights groups in his response to the Belgium attacks when he said Tuesday that authorities should be empowered to "patrol and secure Muslim neighborhoods before they become radicalized."

Both Clinton and Trump seized the attacks on the Brussels airport and subway that left dozens dead as a chance to level bitter assaults on one another.

"This is about not only selecting a president, but also selecting a commander-in-chief," Clinton said in Seattle as she condemned Trump by name and denounced his embrace of torture and hardline rhetoric aimed at Muslims. "The last thing we need is leaders who incite more fear."

Trump, in turn, branded Clinton as "Incompetent Hillary" in an interview with Fox News as he discussed her tenure as secretary of state. "Incompetent Hillary doesn't know what she's talking about," the billionaire businessman said. "She doesn't have a clue."

Clinton and Trump's Republican rivals piled on with questions about his temperament and readiness to serve as commander in chief, and condemned his calls to diminish US involvement with NATO. Belgium is a NATO ally.

Addressing supporters in Seattle, Clinton said the Brussels attacks were a pointed reminder of "how high the stakes are" in 2016.

"We don't build walls or turn our back on our allies," she said. "We can't throw out everything we know about what works and what doesn't and start torturing people."

Cruz criticized Trump's foreign policy while declaring that the U.S. is at war with the Islamic State group.

"He doesn't have the minimal knowledge one would expect from a staffer at the State Department, much less from the commander in chief," the Texas senator told reporters. "The stakes are too high for learning on the job."

Trump's brash tone appeared to turn off some Republican voters in Utah, where Cruz claimed more than half of the caucus vote — and with it, all 40 of the state's delegates.

Yet that wouldn't make up for Trump's haul in Arizona, where he earned all of the state's 58 delegates.

Trump is still short of the majority of delegates needed to clinch the nomination before the party's national convention this summer. But he has a path to the nomination if he continues to win states that award all or most of their delegates to the winner.

The remaining Republican candidate, Ohio Governor John Kasich, was shut out Tuesday.

Overall, Trump has 739 delegates, Cruz has 465 and Kasich 143. It takes 1,237 delegates to win the Republican nomination.

On the Democratic side, Clinton's delegate advantage is even greater. Including superdelegates, or the party insiders who can support whoever they like, she leads the Vermont senator 1,681 to 927. A candidate needs 2,383 delegates to capture the nomination.