I'm not sure what you specifically mean by "such a registry", but if you read further, he clarifies his comments to MSNBC by saying he means a registry for Syrian refugees.

After Trump’s tweet, Fox News asked him about his position on a Muslim registry.

"Let's hear it directly from you," said host Kimberly Guilfoyle. "Would President Donald Trump support a full Muslim database?"

"Basically the suggestion was made and (it’s) certainly something we should start thinking about," Trump said, repeating that the reporter presented the idea. "But what I want is a watch list. I want surveillance programs. Obviously, there are a lot of problems. … But, certainly, I would want to have a database for the refugees, for the Syrian refugees that are coming in because nobody knows where they're coming from."

Guilfoyle followed up: "So to be clear, you are not saying anything with respect to a religious database. You are talking about the Syrian refugees in light of the national security development affecting this country as we speak here tonight."

Trump said he didn’t hear the MSNBC reporter’s question clearly, "but even if I did, I mean, I want databases for the Syrian refugees that Obama is going to let in if they come in."