"[We're] committed to allowing ... people to buy health insurance the way we buy life insurance, the way we buy car insurance," Pence said in a "Squawk Box" interview.
"That is across state lines in a competitive marketplace, not with the top-down government takeover of health care which is what Obamacare was from the very beginning," he said.
Trump wants to replace Obamacare with health savings accounts, a way to put tax-free money aside to pay for medical expenses.
Pence also argued that Trump's outrage over his "stolen" tax records is justified, and it's not hypocritical to use the information contained in Clinton's emails.
Not all the Clinton emails were the result of WikiLeaks publishing hacked files, Pence said, adding some were brought to light by Freedom of Information Act requests.
"Many in the national media are buying into the argument from the other side that the issue here is where they came from, not what's in the emails," Pence said.
"One of the things that's appealing about Donald Trump is that he speaks his mind; speaks it plainly," he said. "I think expressing skepticism on that [merger], as policymakers in Washington, D.C., evaluate that merger was more than appropriate."