Is Trump lying about Muslim database?

Earlier this week Donald Trump suggested in an interview with Hunter Walker of Yahoo News that he was open to a database or registration system for for Muslims in the U.S. “We’re going to have to do things that we never did before. And some people are going to be upset about it, but I think that now everybody is feeling that security is going to rule,” Trump said. “And certain things will be done that we never thought would happen in this country in terms of information and learning about the enemy. And so we’re going to have to do certain things that were frankly unthinkable a year ago.” Trump was asked about it again by NBC News while campaigning in Iowa and didn't contest the idea. Trump took to Twitter today (see below) to say he didn't suggest the idea. Do you think Trump is being honest or is he a liar - pants on fire?