Mitt Romney scored a hard-fought triumph in his native state of Michigan and powered to victory in Arizona today, dealing a blow to his chief rival and gaining precious momentum in the turbulent Republican presidential race.

Mr Romney's victories cement his status as his party's front-runner to challenge President Barack Obama in the November election, and injects his campaign with new energy ahead of next week's crucial contests in 10 states, known as Super Tuesday.

Rick Santorum had needed a win or a very close second to show that he was still in play and that victories earlier this month in Minnesota, Colorado and Missouri were not a fluke.

Mr Romney is viewed as the candidate best positioned to beat Mr Obama, and he has the backing of much of the Republican establishment.

But Mr Santorum has captured the heart of the party's conservative base, which has no doubt about the authenticity of his views on social issues such as abortion and considers Mr Romney too moderate.

"We didn't win by a lot but we won by enough, and that's all that counts," Mr Romney told cheering supporters.

Mr Santorum said he would continue his presidential bid, pushing an economic message.

He is telling supporters that a month ago, in his words, "they didn't know who we are, but they do now".

Mr Santorum got distracted from his appeal to working-class voters in recent weeks but sought to refocus during his primary night speech today.

He kept his message on his manufacturing plan, which gave him an early lead in Michigan polls. But that lead later collapsed as he was dogged by questions on contraception and women's rights.

In his remarks, Mr Santorum made a point to cite his 93-year-old mother, who earned a graduate degree and earned more money than his father.

With 87% of Michigan's precincts reporting, Mr Romney had 41% to Mr Santorum's 38%. Texas congressman Ron Paul was in third place with 12%, and former House of Representatives speaker Newt Gingrich was bringing up the rear with 7%.

In Arizona with 62% of precincts reporting, Mr Romney was leading with 48% to Mr Santorum's 26%. Mr Gingrich was third with 16% and Mr Paul came in last with 8%.

Mr Romney's victory in Arizona had been expected, so much so that his opponents spent little time and no money campaigning there.

Mr Romney, a former governor of Massachusetts and ex-chief executive of a private equity firm, has campaigned for the most part by emphasising his business acumen at a time when the US economy is struggling and unemployment remains high.

But the lengthening Republican nomination struggle has coincided with a rise in Mr Obama's prospects for a new term. A survey released during the day showed consumer confidence at the highest level in a year, and other polls show an increase in Americans saying they believe the country is on the right track.

The president is unopposed for the Democratic nomination and timed an appearance before members of the United Auto Workers union in Washington for the same day as the Michigan primary.

He attacked Republican candidates for saying that union members profited from the taxpayer-paid rescue of the car industry in 2008-9, calling the assertions a "load of you know what".

To seal the nomination a candidate must accumulate the backing of 1,144 delegates to win the party nomination at the Republican National Convention in Tampa, Florida, in late August.

Mr Romney picked up all 29 delegates at stake in Arizona to raise his total to 152 delegates, according to the AP's count, compared with 72 for Mr Santorum, 32 for Mr Gingrich and 19 for Mr Paul. Michigan's 30 delegates were to be distributed proportionally.

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