Democrats nominated two women they hope will give them the rare opportunity to capture seats in the Republican-dominated South and potentially spare President Barack Obama from spending the final two years of his presidency dealing with a Congress fully controlled by the opposition.

Michelle Nunn, a non-profit CEO, won the primary Tuesday for the Senate seat long held by her father, Sam Nunn, and now occupied by retiring Republican Saxby Chambliss. Her opponent will be decided in a July 22 runoff between the top two finishers in a seven-candidate race.

In Kentucky, Alison Lundergan Grimes, a state official, will face a tougher challenge in taking on the Senate's top Republican, Minority Leader Mitch McConnell. Both easily defeated their opponents, with McConnell fending off a challenger backed by the small-government tea party movement.

Republicans, who are likely to keep control of the House of Representatives, have strong prospects for capturing the Senate in November. With roughly a third of the Senate's 100 seats on the ballot, they need a net pickup of six seats. Democrats have been hurt by the retirement of some of their longtime senators in states that lean Republican. Also, some Democratic senators who swept into office when Obama was first elected in 2008 are now vulnerable as they seek re-election.

Among the Republicans' top targets is the southern state of Arkansas, where the Democratic incumbent, Mark Pryor, won his party's nomination Tuesday. He will face congressman Tom Cotton, who won the Republican nomination.

Primaries critical for Republicans

Democrats are contending with Obama's low popularity and the historic pattern of a president's party generally losing seats in midterm elections. Republicans are making Obama and his troubled health care overhaul the focus of their campaigns.

'I am not an empty dress. I am not a rubber stamp. And I am not a cheerleader. I am a strong Kentucky woman.' - Alison Lundergan Grimes, a state official

The primaries are critical for Republicans, who saw an opportunity to win the Senate slip away in 2010 after party voters repeatedly picked candidates backed by the tea party movement. Many were too conservative or unsteady to win in the general election.

This time, Republican Party leaders and their supporters in the business community are determined to support establishment-backed conservatives in primaries against tea party challenges. McConnell's strong showing in Kentucky with about 60 per cent of the Republican vote Tuesday was noteworthy because that is where the tea party made its mark four years ago by sweeping Rand Paul into the Senate over an establishment candidate favoured by McConnell.

McConnell, a five-term Senator and the embodiment of the Republican establishment, said he would use his power to check Obama's agenda. "Make me the majority leader and Kentucky will lead America," he said in an appeal to home state pride at a victory rally in Louisville.

Meanwhile Grimes, who piled up 76 per cent of the vote to defeat three Democratic rivals, responded forcefully to some of the campaign barbs that have already come her way. "I am not an empty dress. I am not a rubber stamp. And I am not a cheerleader. I am a strong Kentucky woman," she told cheering supporters in Lexington.

In Georgia, the race for the Republican Senate nomination was fiercely expensive — $10 million had been spent on television commercials through last week. Businessman David Perdue, who cast himself as an outsider, and U.S. Rep. Jack Kingston, who drew support from the party establishment, took the top two spots, finishing ahead of several candidates favoured by the tea party movement.

In Oregon, Monica Wehby, a physician, won the Republican nomination to oppose Democratic Sen. Jeff Merkley in a race that Republican strategists hope can become more competitive as the year unfolds.

Gubernatorial primaries in some states

On the busiest day so far this year on the U.S. political calendar, there were also gubernatorial primaries in Pennsylvania, Georgia, Arkansas, Oregon and Idaho.

Democrats hoping for a return to power in Pennsylvania nominated businessman Tom Wolf to oppose the vulnerable Republican Gov. Tom Corbett, whose poor showing in polls drew a crowded field in the Democratic gubernatorial primary's bid for a second term.

In Georgia, Jason Carter, a state senator and grandson of former president Jimmy Carter, was unopposed for the Democratic nomination. Republican Gov. Nathan Deal easily defeated two primary challengers.

Arkansas primary voters set up a race between Republican Asa Hutchinson, a former congressman who also served in the Bush organization, and former Democratic Rep. Mike Ross.

A smattering of Republican House members faced primary foes, notably Rep. Mike Simpson of Idaho, who won handily despite a tea party-backed challenge.

In Pennsylvania, Chelsea Clinton's mother-in-law, former Rep. Marjorie Margolies, lost her bid to return to the House in a district northeast of Philadelphia — despite fundraising and other campaign help from Bill and Hillary Rodham Clinton.