"We're on our way," Romney told supporters in a ballroom in the Westin Hotel in Boston, with his wife Ann beaming proudly at his side. "I'm not going to let you down. I'm going to get this nomination."

At a "victory" party in Steubenville, Ohio, Santorum loyalists cheered after he won Oklahoma, but the late Ohio loss was to leave a sour taste in their mouths.

Santorum, 53, a devout Roman Catholic who fiercely opposes abortion and gay marriage, has billed himself as the only authentic conservative in the race who understands working-class voters and can beat Obama in the fall.

"We have won in the West, the Midwest and the South and we're ready to win across this country," he told an ear-splitting rally.

But Santorum's radical views have alienated some moderates, and after the Ohio setback serious questions will be asked about his electability.

Romney, 64, won a majority of the 10 states in play, but lingering doubts remain as he has struggled to win in the South, with Santorum and Gingrich sweeping Georgia, Tennessee and Oklahoma.

The mixed bag of results means there is still a long way to go in the state-by-state battle ahead of the Republican convention in August, when the party's nominee will be crowned.

In Dublin, Ohio, Mark Kraft -- wearing a red, white and blue American flag shirt -- said he had faced a tough choice.

"At the last minute I did vote for Santorum," the 51-year-old media monitor said. "It was like (the children's game) 'rock-paper-scissors' in my head."

Hank McCormick, 65, voted for Romney and attacked Obama for failing to deliver as hard-hit states like Ohio struggle to emerge from a painful recession with a stubbornly high unemployment rate of 8.3 percent.

"I want a businessman in there, someone who understands profit and loss and who can beat the opponent," he said. "Three and a half years ago, everybody was looking for some change. Now I'm looking for a reverse."

Delegates are awarded by each state in the complex Republican Party nominating process, with one candidate needing to reach 1,144 delegates to declare victory.

Romney was projected to extend his delegate lead but still faces a long march to the nomination. He has now won 14 states, while Santorum has won seven and Gingrich two. Texas Congressman Ron Paul has yet to notch up his first win.

Romney leads with an estimated 404 delegates, followed by Santorum with 165, Gingrich with 106 and Paul with 66, according to a CNN tally early Wednesday.

But despite Romney's victory in a majority of states and his comfortable delegate lead, few analysts saw Tuesday as a stunning success for him.

"I wish I could say that this is a better night for Mitt Romney,"

Republican campaign consultant Brad Marston told AFP as the votes were still rolling in Tuesday night.

"I don't think he takes a lot of momentum out of tonight," he said, adding that Romney was nonetheless sure to ultimately win the nomination.

Romney meanwhile vowed to soldier on in the months-long process he has mostly dominated but still not wrapped up.

"We'll go day by day, step by step, door by door, heart to heart. There will be good days, there will be bad days," he told supporters here Tuesday night.

"But on November 6th, we're going to stand united. Not only having won an election, but having saved a future."