Florida Sen. Marco Rubio challenged Donald Trump at a Republican presidential debate Thursday to give more details about what he would put in place of the Affordable Care Act, but the front-running businessman said only that he would allow people to buy health insurance across state lines.

“What is your plan on health care? You don't have a plan,” said Sen. Rubio, who advocated allowing employers to give their workers tax-free funds to buy health savings accounts or private insurance. Others would be able to buy coverage with a refundable tax credit, Sen. Rubio said.

Mr. Trump said allowing plans to be sold across state lines would “solve a lot of the problem” by improving competition, and when asked if there was more he wanted to express, said “there's nothing to add.”

Analysts have been skeptical that allowing interstate sale of health policies, a frequent Republican demand, would lower prices or support robust plans.

The debate at the University of Houston was the final one before next week's Super Tuesday, when more than a dozen states have their primaries. It was more contentious than previous debates as Sen. Rubio and Texas Sen. Ted Cruz spoke over one another and Mr. Trump in an effort to pull themselves closer to the lead.

Sen. Cruz also attacked Mr. Trump on health care by saying Mr. Trump supported “socialized medicine,” which Mr. Trump quickly denied.

Mr. Trump has been vague about how health insurance should work, only saying he would “take care” of people. He recently walked back his comment “I like the mandate," which he said during an interview, by saying he would repeal all of the ACA.

Sens. Cruz and Rubio said the ACA has cost jobs and cut hours for many Americans, although the data analyzed has not borne this out.

Sen. Cruz also said he would have the U.S. Justice Department investigate Planned Parenthood, which Mr. Trump had previously praised for offering care to millions of women. Mr. Trump also said, however, that he would pull funding for the organization because it provides abortions in some states. There is already a ban on any federal funding being spent on abortion.

Mr. Trump again repeated his claim that insurance companies are “making a fortune” under the ACA, although some companies have said they are losing money and economists have not previously supported the statement.

Ohio Gov. John Kasich, who is lagging in the polls, outlined a plan for replacing the ACA that would pay providers for quality of care and incentivize them to lower prices. Health care charges would also be more transparent, he said.

“This is not a theory,” he said. “This is what we're actually doing in our state.”

Retired neurosurgeon Dr. Ben Carson, whose campaign has hit a brick wall, spoke again of “health empowerment accounts” that would make “every family their own insurance plan.”

Catastrophic plans would cover about 75% of people, he said, adding that they could also choose from a menu of additional coverage options such as in Medicare Part C.

“It would be such a great program that nobody would want Obamacare,” he said.

Shannon Muchmore writes for Modern Healthcare, a sister publication of Business Insurance.