State Senate President David Williams said today that he won't run for the U.S. Senate.

The Lexington Herald Leader reports that in making the announcement, Williams said that he thinks Sen. Jim Bunning (R) will seek re-election. He said the most qualified challenger to the embattled incumbent would be Cathy Bailey, a former ambassador to Latvia. More from the Herald Leader:

Williams said it would be interesting to have a qualified woman in the United States Senate from Kentucky, "someone who has the international experience that she has, and she presents herself very well."

But Williams added that he was not endorsing any particular candidate.

Secretary of State Trey Williams (R) and Rand Paul, son of Texas Congressman Ron Paul, are running in the primary as well. Democrats have a tough primary ahead, with Lt. Gov. Dan Mongiardo and Attorney General Jack Conway seeking the nomination.