WASHINGTON — Phil Bryant, the Republican governor of Mississippi, defied a last-minute appeal from the White House and announced Wednesday that he was appointing Cindy Hyde-Smith, the state’s agricultural commissioner, to fill the seat Senator Thad Cochran is vacating next month.

Appearing at an outdoor rally in Brookhaven, Miss., Ms. Hyde-Smith’s hometown, Mr. Bryant said the decision had been “mine and mine alone” and urged the state’s voters to rally to her side ahead of the special election for the seat this November.

Ms. Hyde-Smith, who would be the first woman in the Senate representing Mississippi — the only state that has not had a female governor or member of Congress — used her remarks to outline her accomplishments in office. Aware that Mr. Trump is uneasy about the strength of her candidacy, she also repeatedly invoked and praised the president, made a reference to his signature slogan (“Make America Great Again”) and recalled she had served on his agricultural advisory team.

And she made an oblique but unmistakable reference to her coming race against State Senator Chris McDaniel, the firebrand conservative who nearly ousted Mr. Cochran in 2014 and is challenging Ms. Hyde-Smith for the seat.