U.S. Republican front-runner Donald Trump swept to victory in Arizona on Tuesday (March 22) but rival Ted Cruz showed some fight with a win in Utah that gave hope to establishment Republicans who fear Trump would lead the party to ruin in the presidential election.

On the Democratic side, favorite Hillary Clinton routed challenger Bernie Sanders in Arizona to stretch her advantage in the race for her party's presidential nomination.

Sanders, however, won contests in Utah and Idaho to bolster his case that he still has a chance despite Clinton's big lead.

The nominating battles in Arizona and Utah, and the Democratic contest in Idaho, were overshadowed by attacks in Brussels in which at least 30 people were killed and raised security concerns among U.S. voters.

Trump helped himself in Arizona with a hardline anti-immigration message and tough talk on Islamic militants to easily defeat Cruz, a U.S. senator from Texas, and Ohio Governor John Kasich.

Trump had the backing in Arizona of Maricopa County Sheriff Joe Arpaio, one of the most prominent supporters of a crackdown on illegal immigrants.

The win furthered Trump's argument that he will eventually win the Republican presidential nomination and that the party should rally around him. He won all of Arizona's 58 delegates.

Cruz, though, won big in Utah's caucuses, giving hope to those Republicans who fear Trump's proposal to deport 11 million illegal immigrants and build a wall on the U.S. border with Mexico would guarantee a Democratic victory in the November 8 election.

Cruz appeared to be on track to win all of Utah's 40 Republican delegates. Since the state's 40 delegates are awarded proportionate to the popular vote, he needed to win at least 50 percent of the vote to take all the delegates.

sanders Democratic U.S. presidential candidate Bernie Sanders holds a town hall event at the Navajo Nation casino in Flagstaff, Arizona, March 17, 2016. Photo: Reuters/Nancy Wiechec

Sanders said his Utah and Idaho victories were powered by young people and working-class Americans who support his "political revolution." 

Trump is trying to beat back efforts to deny him the nomination. His opponents want to stop him from securing the 1,237 delegates needed ahead of the July convention. Trump now has 678 delegates.

Sanders is looking for wins in many of the six Democratic contests this week. Alaska, Hawaii and Washington will vote on Saturday. Clinton will keep adding to her delegate total even if she is not the winner in a given state because Democratic delegates are awarded proportionally in all states.

Tuesday's Republican contests were the first since U.S. Senator Marco Rubio of Florida dropped out a week ago after Trump drubbed him in his home state.

Kasich is the only other candidate still in the race, splitting the anti-Trump vote with Cruz.