"This is horrible, a declared Nazi candidate for Congress For the good people of Illinois, you have two sensible choices: Write another candidate or vote for the Democrat, this bigoted idiot should get zero votes", Cruz, a Texas Republican, wrote on Twitter.
"You have not submitted a third-party candidate?" Jones asked a Politico reporter during a phone call. "That's great! That's awesome!"
Jones went on to say that he "snookered" the Illinois GOP, according to Politico.
Earlier this year, the Republican Party of Illinois condemned Jones's campaign and said there was "no room for Nazis like Arthur Jones" in the GOP or in the country.
"The Republican Party of Illinois and our country have no room for Nazis like Arthur Jones, and we are strongly opposed to his racist views and candidacy for any public office, including the 3rd Congressional District," said the Republican Party chairman Illinois, Tim Schneider, previously in a statement.
In November, Jones will face the Democratic incumbent, Rep. Dan Lipinski.
Lipinski is an anti-abortion Democrat who has lived in the district for more than a decade. He is strongly favored to win.