In an interview in his Senate campaign office here, Portman said it is wrong for Trump to make an issue of someone's background.
"The fact that the judge has a Mexican American heritage has nothing to do with how you should describe his judicial ability. The guy was born in Indiana. He’s as American as I am," said Portman, who was born and raised in Ohio.
"Even if he were an immigrant, I would feel the same way about it, but he’s an American," Portman said. "It’s wrong to make an issue of ethnicity or heritage."
The senator, who has been floated to be among Trump's potential vice-presidential picks, said he would decline the position if it were offered.
Portman, who is in a tight reelection race with Democrat Ted Strickland, said he is focused on the state and probably isn't the best person to be Trump's No. 2.
"I disagree with him on a number of issues, and that would be awkward," Portman said.
Trump's attacks on Curiel are a "distraction from what we should be talking about, which is this incredibly weak economy," the senator said, referring to Friday's weak jobs report.
"I’m not suggesting he should tone it down in terms of the jobs report; he should talk more about that," Portman said. "But with regard to this issue of the ethnicity of a judge, yeah, that should not be relevant."
Portman said he still will support Trump's campaign because of the candidate's stance on economic issues and his promises to create more jobs.
"What Donald Trump talks about in terms of tax reform, regulatory reform, all those issues are going to give the economy a shot in the arm if we put them into practice," he said. "I’m also very concerned about Hillary Clinton’s economic reform policy and where she would take the country."
Strickland's campaign blasted Portman's remarks.
"Senator Portman’s simultaneous endorsement and condemnation of Donald Trump is exactly the kind of spineless, self-interested politics that Ohioans hate about Washington insiders," Strickland spokesman David Bergstein said in a statement. "Each day Portman twists himself further and further into a tortuous pretzel as he stubbornly continues to back Trump’s campaign."