Polls have closed in the northern U.S. state of Michigan, after a tight battle between Republican presidential hopefuls Mitt Romney and Rick Santorum.

Romney fought hard to fend off Santorum, who has surged in the polls and had a three-state victory earlier this month in Colorado, Minnesota and Missouri. The two were virtually tied in opinion polls.

Romney once held a commanding lead in Michigan, the state where he was born and where his father was a popular governor.

The soutwestern state of Arizona also voted Tuesday to pick a Republican candidate to face President Barack Obama, a Democrat, in the November election. Romney enjoyed a clear lead in Arizona.

Romney and Santorum could end up splitting Michigan's delegates because the state awards them based on the proportion of the vote. Arizona is a winner-take-all contest.

Romney, a former Massachusetts governor, is having difficulty winning the support of social conservatives, who are rallying behind Santorum.

Texas Representative Ron Paul and former House speaker Newt Gingrich are far behind in the polls. Gingrich turned his campaign efforts Tuesday to Georgia, a state he represented in Congress for two decades. Paul held an evening campaign rally in Virginia.

Romney and Santorum made last-minute appeals in Michigan for support, with campaign events across the state. Santorum is hoping a victory will cement his status as the conservative alternative to Romney, while Romney is seeking to boost campaign momentum and reclaim front-runner status.

The primaries come a week before the much-anticipated “Super Tuesday,” when 10 states hold presidential nominating contests.