For decades Republican leaders vowed to recruit more minority candidates and tried to project a “big tent” image for the party, and in recent years they saw some payoff with governors: Bobby Jindal of Louisiana and Nikki Haley of South Carolina, both Indian-Americans who have since moved on, and Brian Sandoval of Nevada and Susana Martinez of New Mexico, both Hispanic-American.

But in the first midterm elections under Donald J. Trump, whose campaign and presidency included strong appeals to white voters, Republicans have no black or Hispanic nominees for governor in 2018, and few from other racial minorities, in the 36 states holding elections for the position. The overwhelming majority are white men.

And with Mr. Sandoval and Ms. Martinez leaving by early January, Republicans are at risk of having an all-white bench of governors in 2019.

Democrats this year, by contrast, have nominated black, Hispanic and Native American candidates for governor in Arizona, Florida, Georgia, Idaho, Maryland and elsewhere. This lineup comes after years when Democrats were weak on diversity in governors’ races.