Republican presidential candidate and former Massachusetts Governor Mitt Romney shows his ballot to his wife Ann while voting in Belmont, Massachusetts March 6, 2012. [Photo/Agencies]

STEUBENVILLE, Ohio - Mitt Romney notched early wins as he fought to establish his dominance in the race for the Republican US presidential nomination on Tuesday but looked unlikely to score a knockout blow that would force any of his rivals from the contest.

Rick Santorum scored convincing wins in Oklahoma and Tennessee, while Ohio, the biggest prize of the night, was too close to call.

Romney won as expected in Virginia, Vermont and his home state of Massachusetts as 10 states held contests on "Super Tuesday," the biggest day so far in the roller coaster Republican campaign.    

Newt Gingrich won his home state of Georgia, while results from North Dakota, Idaho and Alaska were expected in the coming hours. More than 400 of the 1,144 delegates needed to win the party's nomination are at stake.

All eyes were on Ohio, a traditional bellwether state that could play an important role in deciding the Republican nominee to challenge Democratic President Barack Obama on Nov 6.

Exit polls showed that Ohio voters viewed Romney as more likely to defeat Obama, but thought Santorum was more sympathetic to average Americans' concerns.

With 22 percent of the vote counted, Santorum edged ahead but the two were still neck-and-neck.

A victory in Ohio and a good showing elsewhere would make Romney, a former Massachusetts governor, the favorite to win the nomination. Even without an Ohio win, his strength in other states all but ensures he will extend his lead in the delegate count.

"This is a process of gathering enough delegates to become the nominee, and I think we're on track to have that happen," Romney said after voting in his home town of Belmont, Massachusetts.

A less impressive showing could prompt renewed doubts about his ability to secure the nomination as Republicans continue the state-by-state battle to pick a nominee at their August convention.

Romney, who built a fortune of at least $200 million as a private-equity executive, has struggled to connect with conservatives and blue-collar voters.

"He doesn't really know what he stands for," said Santorum supporter Katherine Frenz, 36, of Hilliard, Ohio.

In the last days of the Ohio campaign Romney made a point of trying to attract blue-collar voters, but CNN's exit poll indicated that Santorum received more support among the middle-income voters who make up the bulk of the electorate. Romney topped Santorum among voters with income of more than $100,000, while those who earned less than $30,000 were divided between the two candidates.