US Republican front-runner Donald Trump has swept to victory in Arizona but rival Ted Cruz showed some fight with a win in Utah, giving hope to establishment Republicans who fear Mr Trump would lead the party to ruin in the presidential election.

Key points: US networks project big wins for Trump and Clinton in Arizona

US networks project big wins for Trump and Clinton in Arizona Trump lags behind Ted Cruz in Utah

Trump lags behind Ted Cruz in Utah Democratic contest also in Idaho

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

However, Mr Sanders won contests in Utah and Idaho to bolster his campaign.

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

Long lines of voters were reported in both Arizona and Utah.

In Arizona, a state bordering Mexico, Mr Trump's hardline immigration message is popular and he leads in polls.

However in Utah, Mr Cruz was far ahead, appearing to benefit from Mormons who dominate the Republican vote there.

They did not take kindly to a Trump attack on native son Mitt Romney, the 2012 Republican nominee who has led the anti-Trump opposition.

Donald Trump has won the Republican primary in Arizona. ( Reuters: Scott Audette )

The New York billionaire and former reality TV star has ridden an anti-Washington message to become the favourite for the Republican nomination.

This has left a flagging anti-Trump effort with faint hopes of stopping him at the Republican national convention in July.

On Monday, the billionaire warned against efforts to deny him the nomination if he falls short of securing the 1,237 delegates needed ahead of the July convention.

He now has 678 delegates.

"I think it is going to be very hard for them to do," he said on CNN of any effort to deny him the nomination if he falls short.

"I have millions of votes more than anybody."

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

Meanwhile, Bernie Sanders is looking for wins in many of the six Democratic contests this week, with Alaska, Hawaii and Washington to vote on Saturday.

However, because Democratic delegates are awarded proportionally in all states, Mrs Clinton will keep adding to her delegate total even if she is not the winner in a given state.

The two nominees from each party will eventually meet in the November 8 election for US president.

AFP/ Reuters