Gov. Phil Bryant outlines his legislative priorities during the State of the State address Jan. 9, at the Capitol in Jackson, Miss. (Rogelio V. Solis/AP)

Mississippi Gov. Phil Bryant (R) will not appoint himself to the Senate seat Republican Thad Cochran will vacate, Bryant’s office said Tuesday, leaving his party’s officials searching for a suitable person to fill the vacancy.

“The governor will serve out his term,” Bryant spokesman Clay Chandler said. “He will not appoint himself to the U.S. Senate, believing it improper to do so.”

President Trump and Senate Majority Leader Mitch McConnell (R-Ky.) had urged Bryant to consider appointing himself, according to people familiar with their conversations. Their appeals did not appear to be swaying Bryant. Tuesday marked the most definitive public statements he and his team have issued.

McConnell, who is defending a 51-to-49 majority in this year’s midterms, is determined to ensure that electable Republicans are in place in key races. Mississippi has presented him with a conundrum as he pursues that goal.

Cochran, who has been battling health issues, announced Monday that he would step down from the Senate on April 1. There will be a special election to fill his seat the same day as the midterm elections on Nov. 6. In the meantime, Bryant has the authority to appoint an interim replacement.

Bryant, who is broadly popular, would have been considered a heavy favorite to hold on to the Cochran seat had he appointed himself and run in the special election to serve the remainder of Cochran’s term, which expires in January 2021.

In the state’s other Senate race, Republican Roger Wicker is running for reelection. He has drawn a primary challenger, state Sen. Chris McDaniel, who is a McConnell foe. But McDaniel has left the door open to running for the Cochran seat instead.

Without a formidable Republican in the race for Cochran’s seat, there is a risk that McDaniel could have the inside track. Not only does he represent a threat to McConnell’s leadership, but also some Republicans believe that his hard-right views could make him vulnerable to losing to a Democrat.

If no candidate receives a majority of the vote in a special election, which will be open to candidates of all parties, the top two finishers would advance to a runoff.

Names mentioned in Republican circles as potential appointments for the Cochran seat include state Agriculture and Commerce Commissioner Cindy Hyde-Smith, Lt. Gov. Tate Reeves and Secretary of State Delbert Hosemann.

Bryant is in his second term, which will expire in 2020.