Referring to Trump as "our Republican nominee," Johnson said he supports him on a number of issues, including securing the border and fighting the Islamic State terrorist group, but that he's also "not going to defend the indefensible."
Johnson's Democratic opponent, former Sen. Russ Feingold, challenged Johnson to renounce Trump, who's been battered by accusations of sexual misbehavior. Trump has denied the allegations.
"This is one of these times where you have to be an American first, not a politician running for office, not a Republican or Democrat, but an American who's worried about the future of our great country," Feingold said.
The presidential race has cast a shadow over Wisconsin's Senate campaign, as Johnson said he supports but does not endorse Trump. He's spoken out against Trump on a number of issues, most recently denouncing his crude comments about women that were captured in a video released last week. Johnson also has not campaigned with Trump in Wisconsin and planned to skip an upcoming rally Trump had planned for Monday in Green Bay, the same city where Friday's debate took place.
"I've not been shy in disagreeing with our candidate, with our nominee. I'm not going to defend the indefensible." Johnson said during the debate.
Feingold challenged Johnson to follow the lead of other Republican senators in tough re-election fights, including Arizona Sen. John McCain, in not supporting Trump.
"He doesn't have the temperament to be president," Feingold said of Trump. "He's used divisiveness, saying horrible things about various ethnic groups and others in this country to get himself the nomination. And it appears he's done a lot of other inappropriate things. This is no person to be a role model for the people of our country. Frankly, I think it will be very frightening for the rest of the world if we elected Donald Trump."
Feingold supports Democrat Hillary Clinton and has curried favor with the more liberal wing of the party by campaigning with Vermont Sen. Bernie Sanders and Massachusetts Sen. Elizabeth Warren this month.
Johnson said Friday that Clinton was "completely disqualified from being president" because of how she handled the Benghazi attacks that left four Americans dead and her use of a private email server while she was secretary of state.
Johnson said Feingold "must be the last American who thinks Hillary Clinton is trustworthy."
Feingold and Johnson are familiar debate opponents: They squared off three times in 2010, a race Johnson won, ending Feingold's 18-year run in the Senate.
Democrats see Johnson as vulnerable in a presidential election year when Democratic turnout in Wisconsin is expected to be strong. A Marquette University Law School poll released this week showed the race to be about even.
Unlike with the presidential debates, neither Feingold nor Johnson interrupted each other during Friday's hourlong contest sponsored by the Wisconsin Broadcasters Association. Both also refrained from hurling the type of insults that have become common in the presidential race, though they did have sharp disagreements.
Feingold took Johnson to task for claiming that Feingold as a senator had known about problems at the Veterans Affairs medical facility in Tomah but did nothing. Feingold said Johnson was "saying something he knows isn't true" about when Feingold found out about the over-prescription of drugs at the Tomah VA.
Feingold pledged to fight to raise the federal minimum wage, require paid medical leave, oppose the Trans-Pacific Partnership trade deal, work to fight climate change and allow college students to refinance student loan debt.
Johnson branded Feingold a "career politician" whose solution to every problem is growing government. Johnson, who built a plastics manufacturing company in Wisconsin before being elected to the Senate six years ago, said his private business background makes him more qualified to know what policies will work to create jobs and spur economic development.