NOVI, Michigan (AP) -- Mitt Romney scored a hard-fought victory in his native state of Michigan and won handily in Arizona, slowing the advance of his top Republican presidential rival Rick Santorum and gaining precious momentum ahead of a key set of primary contests next week.

Romney's sweep of Tuesday's contests marked the latest turn in a turbulent Republican primary campaign, and could cement his status as his party's front-runner to challenge President Barack Obama in the November presidential election. But he fell short of landing the knock-out punch needed to stop his top opponent in his tracks.

Romney is viewed as the candidate best positioned to beat Obama, and he has the backing of much of the Republican establishment as well as more campaign funds and a stronger organization than his primary rivals. But 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 Romney too moderate and inconsistent.

``We didn't win by a lot but we won by enough, and that's all that counts,'' Romney told cheering supporters in Michigan on Tuesday night.

``On to the March contests,'' he said, looking ahead to next week's 10 Super Tuesday races that could go a long way toward determining the Republican who will take on Obama.

Santorum had hoped for a win in Michigan following his victories earlier this month in Minnesota, Colorado and Missouri. He told supporters late Tuesday that a month ago ``they didn't know who we are, but they do now.''

The former senator from Pennsylvania was already campaigning in Ohio, one of next week's biggest prizes, when the verdict came in from Michigan, and vowed to stay the conservative course he has set. Romney will campaign Wednesday in Ohio before he flies to North Dakota.

Two other candidates in the race, former House Speaker Newt Gingrich and Texas Rep. Ron Paul, made little effort in either Michigan or Arizona, focusing instead on Super Tuesday contests. Gingrich planned to campaign Wednesday in Georgia, the state he represented in the House of Representatives for 20 years.

With 99 percent of Michigan's precincts reporting, Romney had 41 percent to Santorum's 38 percent. Paul was in third place with 12 percent, and Gingrich was bringing up the rear with 7 percent.

In Arizona with all precincts reporting, Romney led with 47 percent to Santorum's 27 percent. Gingrich was third with 16 percent and Paul came in last with 8 percent.

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

Michigan was as different as could be, and turned into an expensive battle that Romney _ whose father was governor there and headed a now-defunct auto company _ could ill afford to lose and Santorum made every effort to pull off an upset win.

In interviews as they left their polling places, Michigan voters expressed a lack of enthusiasm about their choices. Just 45 percent said they strongly favored the candidate they voted for, while 38 percent expressed reservations and 16 percent said they made the choice they did because they disliked the alternatives.

Romney, a former governor of Massachusetts and ex-CEO of a private equity firm, has campaigned for the most part by emphasizing his business acumen at a time when the U.S. economy is struggling and unemployment remains high.

He turned his focus back to Obama in his victory speech Tuesday, and signaled that he intends to stick to his core campaign message of fixing the economy and reducing unemployment in a country still recovering from the worst recession in decades.

``More jobs, less debt and smaller government _ you're going to hear that'' over and over in the states ahead, he said.

Exit polling showed a plurality of Republican voters in both Michigan and Arizona saying the most important factor to them in the primaries was that a candidate be able to beat Obama in November. Romney won that group in Michigan, where it mattered most, and also prevailed among voters in the state who said experience was the quality that mattered most.

Santorum ran particularly well among voters who cited a desire for strong conservatism or strong moral character.

But the long and increasingly harsh campaign, in which Gingrich and Santorum have challenged Romney as insufficiently conservative, has prompted some Republican officials to express concern about the party's chances of defeating Obama in the fall.

The lengthening Republican nomination struggle has coincided with a rise in 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 auto industry in 2008-9, calling the assertions a ``load of you know what.''

Romney picked up all 29 delegates at stake in Arizona's winner-take-all primary. Michigan's 30 delegates were to be distributed proportionally. Romney and Santorum each won at last 11 delegates, with eight delegates left to be awarded.

In the overall race for delegates, Romney has 163 delegates, including endorsements from Republican National Committee members who automatically attend the party's national convention and can support any candidate they choose. Santorum has 83 delegates, Gingrich has 32 and Paul has 19. It takes 1,144 delegates to win the Republican nomination for president at the party's national convention in Tampa, Florida, in late August.

There are 40 delegates at stake in the Washington state caucuses on Saturday, followed by 419 on Super Tuesday, including big state primaries in Ohio and Georgia.