Republican Donald Trump and Democrat Hillary Clinton won their parties' primaries in Arizona on Tuesday, the first results in a night of contests that could see the frontrunners extend their leads in the US presidential race.

The battle shifted westward as voters in Utah and Idaho also were making their picks in a narrowing presidential contest dominated by Trump and Clinton.

"Much bigger win than anticipated in Arizona. Thank you, I will never forget!" Trump posted on Twitter.

With only partial results in, US networks projected the real estate magnate winner with about 46 percent of the vote, compared to 22 percent for Senator Ted Cruz of Texas and 10 percent for Ohio Governor John Kasich.

Clinton was projected to win by an even larger margin, with 60.5 percent compared to 36.9 percent for Senator Bernie Sanders.

The voting gives the candidates another opportunity to pile up delegates on the way to the party nominating conventions, but is not expected to alter the basic outlines of the race.

At stake Tuesday were 98 delegates in the Republican contests in Arizona and Utah, and 131 for Democrats who, unlike the Republicans, also caucus in Idaho.

At this point in the Republican race, Trump's main objective is to amass the 1,237 delegates needed to win his party's nomination outright, and thwart a bid by the party establishment to stop him.

With his victory, Trump snags all 58 Arizona delegates, pushing him closer to the magic number.

That puts Trump at 741 delegates, compared to 421 for his main rival Cruz and 145 for Kasich, according to a CNN tally.

Democrats award their delegates proportionally, with Clinton due to take the lion's share in Arizona.

The deadly attacks in Brussels changed the tone of voting day from the start, with Trump and his main rival Cruz seizing the moment to bash President Barack Obama's foreign policy -- and tout their own tough stances on immigration.

Anyone who tries to attack the United States will "suffer greatly," Trump said, in typically blunt tones that have shaped his populist run for the White House, propelling him from outsider to firm favorite for the Republican ticket.

"Belgium is a horror show right now. Terrible things are happening," he said. He also told CNN that Belgian authorities could have thwarted Tuesday's attacks if they had used torture against a terror suspect who was captured days earlier.

Cruz used similarly strong language, calling for US law enforcement to be empowered to "patrol and secure Muslim neighborhoods before they become radicalized."

Clinton thanked Arizona for her victory during a Tuesday night speech in Seattle. But she also forcefully denounced her Republican rivals for their strident talk about how they would respond to the Brussels attacks.

"What Donald Trump, Ted Cruz and others are suggesting is not only wrong, it's dangerous. It will not keep us safe," she said.

"We need a president who can provide leadership that's strong, smart, and steady," she added. "The last thing we need are leaders who incite more fear."


Arizona: immigration hot spot

Arizona has long been roiled by passions over immigration, an issue Trump has seized on since launching his campaign with inflammatory accusations that Mexico was sending rapists and other criminals across the border and his promise to build a border wall.

The dynamics are different in neighboring Utah, a predominantly Mormon state where pre-caucus polls show the ultra-conservative Cruz positioned to win.

Cruz has been given a boost by Mitt Romney, the losing 2012 Republican nominee who has led the charge to stop Trump. Utah is home turf for Romney, a Mormon from a prominent family who has encouraged Utah residents to vote for Cruz.

Analysts note that Mormons have voted consistently against Trump elsewhere. The Church of Jesus Christ of Latter-day Saints, breaking with the view of many Republicans, has supported immigration reform.

Utah's 40 Republican delegates are all up for grabs by any candidate who wins a majority in the state caucuses.

Cruz's biggest Utah obstacle may not be Trump but Kasich, who has refused entreaties from Romney and others to stay out of the race to give Cruz a clearer shot at taking all the delegates.

On the Democratic side, Clinton is dogged by an unyielding opponent in Sanders, whose well-funded grassroots campaign is going strong despite a string of losses and the former secretary of state's growing pile of delegates -- 1,656 to his 877 before Tuesday, including super-delegates, according to CNN.

To win the Democratic nomination, 2,383 delegates are needed.

Sanders is expected to do better in Utah and Idaho, states with predominantly white populations.

Republicans were also holding caucuses in the Pacific territory of American Samoa.