"[I] like Chuck Hagel. I served with Chuck Hagel in the United States Senate, but he's the wrong man for this job," said Cornyn on "Fox and Friends."
The Texas lawmaker said Hagel isn't fit to lead the Defense Department because of his positions on a nuclear Iran, direct negotiations with groups such as Hamas and an embrace of "naive ideas like [a] nuclear-free world."
"Which is fine to say, you know — I hope and I wish and I pray that it would be that way, but it's not realistic and it's naive, particularly among the person who's supposed to run American national security and keep the peace," he said.
Hagel has drawn fire from many in his party for his criticism of the Iraq war and the surge, as well as for endorsing Democrats in several recent Senate races.
Sens. John Cornyn (R-Texas), Roger Wicker (R-Miss.), David Vitter (R-La.) and Ted Cruz (R-Texas) said earlier this month that they will vote against Hagel, and almost a dozen others expressed serious concern regarding his nomination.
Cornyn said that he's "worried" that President Obama chose Hagel because he wants to make deep cuts to the Pentagon.
"He's [Obama] not really interested in reining in spending in almost any other area, except national security," Cornyn said.
Earlier this month, Cornyn opposed Obama's pick for CIA chief, threatening to block the nomination of John Brennan until the completion of federal and congressional investigations into unauthorized leaks of classified information by the White House.
“John Brennan has not been absolved of responsibility for the slew of high-level security leaks that have characterized this White House,” Cornyn said in a statement shortly after Obama announced Brennan’s nomination.