Sen. John Thune (R-S.D.) on Wednesday said he isn't running for president in 2016, telling radio host Hugh Hewitt that he's not angling for the job.

"I am not running for president," Thune said.

The South Dakota senator's presidential stock was perhaps at its highest before the 2012 election, when he passed on running. He also told a group of grade-schoolers last year that it wasn't in his plans for 2016, either.

Thune has been climbing the leadership ladder in the Senate, serving as chairman of the Senate Republican Conference since early 2012.

"I know a lot of my colleagues are [running for president]," Thune told Hewitt. "And I think that you have to be  -- you probably have to, if you're gonna get serious about it, get going pretty early."