US presidential candidates Donald Trump and Hillary Clinton won their parties' Arizona primaries Tuesday, although their rivals picked up victories in other western states.

The two front-runners in the US presidential race had been expected to win in Arizona, where illegal immigration is a key issue.

With more than 90 per cent of the vote counted, Trump was ahead on the Republican side with 47 per cent of the vote compared with 25 per cent for his closest rival, US Senator Ted Cruz, state election officials said. Ohio Governor John Kasich had 10 per cent.

The billionaire businessman had been favoured to finish on top and collect all 58 delegates. Trump's strong opposition to illegal immigration appears to have been well received in the border state.

Clinton had 58 per cent of the vote in Arizona compared with 40 per cent for rival Senator Bernie Sanders, with three quarters of the vote counted. The state's 75 delegates will be divided among the two candidates proportionally.

It was a better night for Sanders elsewhere, as he won by large margins both in Utah and Idaho, which are holding caucuses as opposed to the traditional ballot voting of a primary.

Sanders picked up 79 per cent of the vote in Utah and 78 per cent in Idaho.

On the Republican side in Utah, Cruz won by a large margin with 69 per cent of the vote that saw him awarded all the state's 40 delegates. Rivals Kasich and Trump trailed with 17 per cent and 14 per cent respectively.

Trump's brash style, multiple marriages and lavish lifestyle had not been expected to give him much support among church members in the overwhelmingly Mormon state.

Mitt Romney, the 2012 Republican nominee, a Mormon with strong ties to the state where he oversaw the Salt Lake City Olympic Games in 2002, has come out strongly against Trump and urged voters to instead support Cruz.

Overall, Clinton and Trump lead the count of delegates needed to secure their parties' nominations at conventions in July. But each still needs to win many more delegates in state-by-state voting in order to clinch their party's nomination outright.

Trump still faces strong opposition from within the party establishment and could face a challenge at the convention if he fails to win a majority of delegates before the meeting in July.

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