David Duke, a former leader of the Ku Klux Klan, embarked on a campaign on Friday to seek a United States Senate seat as a Republican in Louisiana, where he will try to capitalize on his history of inflammatory speech and on the presidential campaign of Donald J. Trump.

The decision by Mr. Duke, 66, a former state representative whose unsuccessful campaigns include bids for Congress, governor and president, thrust him into a sprawling field for the Senate seat and intensified what was already poised to be a raucous race.

But before Mr. Duke could even file his qualifying paperwork in Baton Rouge, the capital of Louisiana, Republicans there and in Washington were distancing themselves from a campaign they plainly expected to be marked by racism and anti-Semitism.

“I believe in equal rights for all and respect for all Americans,” Mr. Duke said in a campaign video. “However, what makes me different is I also demand respect for the rights and the heritage of European-Americans.”