U.S. presidential hopeful Mitt Romney has victories in two primary contests Tuesday, easily winning Arizona and pulling ahead in the tough battle in his native northern state of Michigan.

Romney thanked cheering supporters Tuesday night for what he described as a “great victory” in the two states. He criticized the policies of President Barack Obama, while pledging to create jobs, get the economy back on track, and reduce debt and the size of government.

Romney fought hard in Michigan to fend off main challenger Rick 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 going into Tuesday's contest.

Romney once held a commanding lead in Michigan, the state where he was born and where his father was a popular governor. He won the state's 2008 Republican primary.

Santorum thanked supporters Tuesday night, acknowledging that a month ago the voters in Michigan didn't even know who he was. He also criticized the policies of President Obama and talked about the economy, cutting federal spending, and decreasing dependency on foreign oil.

Romney, a former Massachusetts governor, is having difficulty gaining support from 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 rally in the eastern state of Virginia.

The primaries come a week before the much-anticipated “Super Tuesday,” when 10 states hold presidential nominating contests to pick a Republican candidate to face President Obama, a Democrat, in the November election.