Saying that his staff "did the wrong thing," Bernie Sanders on Saturday apologized to Hillary Clinton and to his own supporters after his aides improperly accessed proprietary voter lists created by Clinton's campaign. But the Vermont senator also suggested that the issue should have been handled without a public spat between the campaigns and the Democratic National Committee.

Asked by moderators at a Democratic debate held in New Hampshire if Clinton is owed an apology for the incident, which resulted in the firing of a Sanders aide, the senator replied "Yes. I apologize."

"Not only do I apologize to Secretary Clinton, and I hope we can work together on an independent investigation, I want to apologize to my supporters," he added. "This is not the kind of campaign that we run and if I find anybody else involved in this, they will also be fired."

Clinton thanked Sanders for the apology and suggested it was time to "move on."

"Now that I think we've resolved your data, we've agreed on an independent inquiry, I think we should move on, because I don't think the American people are all that interested in this," she said as the audience applauded.

Sanders did express concern that the Clinton campaign may have had access to his own voter files.

"I am not convinced that information from our campaign may have ended up in her campaign. Don't know that, but we need an independent investigation and I hope Secretary Clinton will agree with me on that," he said. Clinton said that such an agreement had already been reached by both camps.

And Sanders said "it does bother me" that the issue was leaked to the media rather than handled privately by the campaigns, noting that a similar breach was resolved quietly earlier this year.

"When we saw the breach two months ago, we did not run to the media and make a big deal about it," Sanders said, adding that the resolution of the problem only came after "many press releases from the Clinton campaign."

Sanders clashed Friday with the Democratic National Committee after revelations that at least four individuals associated with his campaign used a technical glitch to access valuable proprietary voter lists from Clinton's team.

The DNC revoked the campaign's access to the voter database, a vital trove of information used for strategic planning in advance of key primary contests. A furious Sanders camp called that an "inappropriate overreaction" and threatened legal action. The two parties reached a settlement early Saturday morning.

Sanders allies have also cried foul about the DNC's role in the dispute, saying that the party has long put its finger on the scale for Clinton's campaign, including by scheduling the limited number of Democratic debates on weekend evenings, when less-known candidates are less likely to win wide exposure.