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McConnell quickly turned to the general election fight against Grimes, who won the Democratic nomination against nominal opposition, and linked her to Obama and Senate Democratic leader Harry Reid.

"Alison Lundergan Grimes is Barack Obama's candidate," McConnell told supporters at a Kentucky victory party. "There isn't a dime's worth of difference between a candidate who puts Harry Reid in charge and Harry Reid himself."

McConnell won about 60 percent of the primary vote.

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In Georgia, businessman David Perdue and U.S. Representative Jack Kingston were the top two finishers in a crowded Senate primary, beating more conservative Tea Party candidates to qualify for a July 22 runoff for the right to face Democrat Michelle Nunn. The runoff was needed because no candidate finished with more than 50 percent of the vote.

In the Republican Senate primary in Oregon, moderate Monica Wehby beat a Tea Party-backed state representative for the nomination to face Democratic Senator Jeff Merkley. Problems with the state's healthcare exchange have given Republicans hope of victory in the Democratic-leaning state.

U.S. Representative Bill Shuster in Pennsylvania and U.S. Representative Mike Simpson in Idaho also defeated Tea Party challengers in Republican House primaries.

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Pennsylvania businessman Tom Wolf beat U.S. Representative Allyson Schwartz to win the nomination to challenge Republican Governor Tom Corbett in what will be one of November's top gubernatorial races.

Former congresswoman Marjorie Margolies, Chelsea Clinton's mother-in-law, lost her bid to return to Congress from Pennsylvania despite an appearance on her behalf by former President Bill Clinton.

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McConnell wins in Kentucky