(CNN) —  

Illinois GOP Gov. Bruce Rauner denounced the Holocaust denier who’s running for the state’s 3rd Congressional District as a Republican, but declined to endorse his Democratic opponent.

Arthur Jones, a former leader of the American Nazi Party, ran uncontested to be the Republican candidate in the Chicago-area district. His campaign website includes a section titled “Holocaust?” Jones has been involved with anti-Semitic and racist groups since the 1970s, according to the Anti-Defamation League, though he told CNN’s Alisyn Camerota earlier this year that he is no longer formally involved with the Nazi party.

Sen. Ted Cruz, a Texas Republican, had encouraged Illinois voters to “write in another candidate, or vote for the Democrat” in a tweet on Friday.

“That guy (Jones) has no place on the ballot. We tried to kick him off. I called him to get out, and he should get out and we should have someone run against him,” Rauner said in an interview Tuesday with Illinois’ WCIA TV.

He went on to say there is “no room in our politics for a person like that.” Rauner had previously denounced Jones, including in February, when he said, “There is no room for neo-Nazis in American politics. I condemn this man in the strongest possible terms,” according to WCIA.

However, Rauner declined on Tuesday to endorse Jones’ Democratic opponent, Rep. Dan Lipinski, according to WCIA.

“No,” he said in response to a question about whether he would endorse Lipinski, according to WCIA. “The one thing I will say is the person, that guy, Johnson or whatever his name is, should not be on the ballot.”

Politico reported on Friday that the Illinois Republican Party could no longer run a third party candidate because the deadline for qualifying had passed.

Other Republicans have condemned Jones and his candidacy as well.

“The Illinois Republican Party and our country have no place for Nazis like Arthur Jones. We strongly oppose his racist views and his candidacy for any public office, including the 3rd Congressional District,” Illinois Republican Party Chairman Tim Schneider said previously in a statement.

Lipinski is a blue-dog, anti-abortion Democrat who has served the district for more than a decade. He is heavily favored to win.

CNN’s Sophie Tatum and Maegan Vazquez contributed to this report.