WASHINGTON — Mitt Romney muscled his way to victory in two Republican primaries Tuesday, one a lopsided contest in Arizona and the other a must-have, close win in his native state of Michigan over hard-charging rival Rick Santorum.

The wins gave Romney a majority of the day’s delegates, a slowly growing total that could prove increasingly important for the Republican presidential nomination race in the weeks to come.

But Romney failed to deliver the kind of convincing result that would start building momentum and rallying wavering Republicans to his side as his aides had long ago expected.

The tough fight to hold the state instead suggested a wide-open race as the two candidates — with Newt Gingrich waiting in the wings and looking for a Southern comeback — head toward a Super Tuesday showdown next week in 10 states, and perhaps to a longer clash beyond.

The campaign now appears more likely to be a state-by-state, delegate-by-delegate competition rather than an early coronation that would have allowed the winner to turn attention full time to the general election challenge to President Barack Obama.

“Thank you Michigan, what a win,” Romney told supporters in Novi. “We didn’t win by a lot but we won by enough; that’s all that counts.”

Santorum treated his close second-place finish in Michigan as a victory too, signaling it would serve as a springboard to new challenges to Romney.

“A month ago they didn’t know who we are. But they do now,” he told cheering supporters in Grand Rapids. “We came into the backyard of one of my opponents. … The people of Michigan looked into the heart of the candidates, and all I can say is I love you back.”

Former House Speaker Gingrich and Texas Rep. Ron Paul, who did not contest either state, finished far back.

Romney invested heavily in Michigan, emotionally and politically. “Michigan has been my home and this is personal,” he said in an ad.

Yet Romney’s once-wide lead in Michigan gave way to a surge of interest in Santorum, the grandson of a Pennsylvania coal miner and a devout Roman Catholic who worked hard to connect with working-class voters in the industrial state and with evangelical Christians.

By primary day, Romney distanced himself a little from Michigan and downplayed the impact of a possible loss.

“If I were turned down by Massachusetts, where I have lived for the last 40 years and served as governor, that would be a little harder to explain,” the former governor of Massachusetts told Fox Business Network.

Hard fought, the campaign was marked by missteps and mistakes over the last week.

For his part, Romney rolled out a major economic agenda in a largely empty football stadium, then traveled to the Daytona 500 race in Florida only to declare that he has friends who own NASCAR racing teams.

“The candidate sometimes makes some mistakes and so I’m trying to do better and work harder and make sure that we get our message across,” Romney told reporters in his first press conference in three weeks.

Asked if he’d hurt his image with repeated remarks that critics have used to paint him as a wealthy elitist, he said, simply, “Yes.”

He also suggested that he’s faltered because rivals appealed to the party’s base with more vocal criticism of President Barack Obama.

“It’s very easy to excite the base with incendiary comments,” he said. “We’ve seen throughout the campaign that if you’re willing to say really outrageous things that are really accusative and attacking of President Obama, you’re going to jump up in the polls. I’m not willing to light my hair on fire to try and get support. I am what I am.”

Santorum made missteps as well.

He said Sunday that he wanted to “throw up” when he read John F. Kennedy’s 1960 speech assuring voters he believed in the absolute separation of church and state. He told conservative talk show host Laura Ingraham on Tuesday that the comment was a mistake.

Fueled by waves of negative TV ads, the primary contest grew so heated that Michigan’s results were disputed even before the polls closed, thanks to the fact that Democrats were allowed to vote in the open primary by changing their party registration temporarily on the spot.

Self-described Democrats cast about 10 percent of the primary ballots, according to exit polls. Half went to Santorum.