Donald Trump and Hillary Clinton have moved a step closer to a potential general election showdown following victories in the Arizona primary.

Long lines were reported across three states on Tuesday night, as the race for the White House went West for contests in Arizona, Utah and Idaho.

Some voters in Arizona waited nearly three hours to cast their ballot, US media reported.

The contests were overshadowed by the attacks in Brussels, which thrust national security back to the top of the campaign agenda and prompted tough talk from the presidential hopefuls.

Clinton used her victory speech to take aim at her Republican rivals, who she accused of inciting fear.

She said the bombings in Belgium reminded Americans "how high the stakes are" in the 2016 election, adding the US needs a "strong, smart, and above all, steady" commander in chief.

The former Secretary of State said the last thing America needs "are leaders who incite more fear".

Trump, meanwhile, cruised to victory in the southern border state, where anti-illegal immigration and national security sentiments run high.

Ahead of the election results on Tuesday, he tweeted: "I have proven to be far more correct about terrorism than anybody - and it's not even close."

The Arizona win gave the brash billionaire another 58 delegates, padding his lead over rivals Ted Cruz and John Kasich.

Both are trying to stop Trump from reaching the 1,237 delegates needed to secure the nomination.

After pocketing the Arizona delegates, Trump has 739 overall, while Cruz and Kasich sit at 425 and 143, respectively.

Cruz hopes win in Utah to block Trump from making a clean sweep on Tuesday. 

The state's 40 delegates are winner-take-all if the winning candidate can earn more than 50% of the vote. If not, the delegates are handed out in proportion to the vote.

Trump, who is already looking ahead, tweeted that he hoped his latest win would unify the Republican party.

Conservative Phoenix Sheriff Joe Arpaio, who endorsed Trump, told the AP news agency that the property magnate's victory should demonstrate to the Republican establishment that it should back off its opposition to the front runner.

Republicans are also holding a caucus in Utah on Tuesday, where 40 delegates are at stake.

Clinton, meanwhile, added 45 delegates from Arizona to pad her lead over Bernie Sanders.

But the Vermont senator did not go quietly, grabbing a victory in Utah, where 33 delegates were at stake.

Idaho was also holding a Democratic contest on Tuesday.

Some 2,383 are needed to secure the Democratic nomination. 

(Sky News)