Bobby Jindal speaks during the CNBC Republican presidential debate at the University of Colorado, Wednesday, Oct. 28, 2015, in Boulder, Colo. (AP Photo/Mark J. Terrill)

Louisiana Gov. Bobby Jindal (R) on Friday challenged his 2016 rival, Sen. Ted Cruz (R-Tex.), to a one-on-one debate next week in Milwaukee, a move that highlights the intensifying competition for the support of conservatives.

[Inching up in Iowa, Bobby Jindal leaves no room on his right]

Rather than targeting the GOP front-runners, businessman Donald Trump and retired neurosurgeon Ben Carson, Jindal is seeking to contrast himself with Cruz, who presents a more direct threat in Iowa, where both men are battling within a crowded field for evangelical caucus-goers.

“He said he’ll debate anyone, anytime, so let’s do it in Milwaukee,” Jindal said in an interview with The Washington Post. “I’m happy to do it.”

Jindal pointed to Cruz’s recent comments on Fox News as the impetus for calling him out. “I’m happy to have as many debates as we can,” Cruz said on Wednesday. “I’m happy to debate anywhere, anytime."

[Cruz: 'Not interested' in signing demand letter on debates]

Jindal said he’d like his debate with Cruz, if it ever happened, to focus on their plans for replacing President Obama’s health-care law. He also questioned the significance of Cruz’s efforts in 2013 to shut down the government.

“You get Ted Cruz who wants to shut down the government, but he’s never even come up with his own plan,” Jindal said. “We’ve written our own plan and campaigned on it, rather than just complaining about Obamacare.”

Both Cruz and Jindal will be in Wisconsin on Tuesday to participate in Fox Business Network debates. Cruz will be on the main stage, Jindal in the “undercard” debate.

Cruz's campaign would not comment on Jindal's request.