Donald Trump’s latest media and political firestorm stems from ambiguous answers to a reporter's question: Whether he would support making Muslims register in a national database.

But his comments are not quite as cut-and-dried as the headlines declaring his support for the registry would make them seem. And by Friday, Trump clarified -- on Twitter, his favorite forum for taking on the media -- that he never suggested such a thing.

Trump continued to clarify his comments on Fox News’ “On The Record” telling host Kimberly Guilfoyle late Friday that he was “really responding to a totally different reporter.”

“He was responding to that reporter where basically the suggestion was made and it’s certainly something we should start thinking about but what I want is a watch list, I want surveillance programs,” Trump said. “I want a database for the Syrian refugees that Obama is going to let in.”

Trump told Guilfoyle that letting Syrian refugees into the United States is a “Trojan horse” and that “plenty of problems are going to be caused.”

“We are very, very foolish in this country and we have a lot of problems and the biggest problem we have no leader.”

The headlines started after Yahoo News published an article Thursday based on an interview with the Republican presidential candidate. The reporter apparently asked Trump whether new security measures might involve a database to register Muslims in the U.S.

When he replied, “We’re going to have to — we’re going to have to look at a lot of things very closely” including mosques, Yahoo News reported that Trump did not “rule [the database] out.”

He was then asked by CNN whether he would rule out such a database, to which Trump said he “never responded to that question” during the Yahoo News interview.

But a separate exchange with NBC News muddied the picture of his position further.

The reporter initially asked Trump whether there should be a database to track Muslims.

“We should have a lot of systems,” Trump responded, but then went on to tout the importance of a strong border and a border wall. Asked whether he would like to implement that, Trump responded:

“I would certainly implement that. Absolutely.”

That single line was swiftly interpreted in several news stories as Trump’s endorsement of a database for Muslims, in turn prompting a widespread backlash. Some stories even stated that Trump had proposed a “plan” to register Muslims in a database.

However, in the NBC News exchange, Trump appeared to be referring in that single line to border and immigration security measures, because he then said the effect would be, “It would stop people from coming in illegally.”

Yet the reporter went on to ask Trump directly, once again, about a database for Muslims, and Trump did not dismiss the idea.

Instead, when asked how to do it, Trump said: “It would be just good management.”

Asked if those running it would have to go to mosques, he said: “Different places. You sign them up … but it’s all about management.”

Asked for clarification, the campaign referred FoxNews.com on Friday to Trump's latest tweet.

Trump has meanwhile been the subject of heated and bipartisan criticism since the remarks were published.

Hillary Clinton tweeted a link to a New York Times story reporting that Trump said he “absolutely” would require Muslim registration.

"This is shocking rhetoric. It should be denounced by all seeking to lead this country," she tweeted.

Republican candidates also slammed Trump. Former Florida Gov. Jeb Bush called the plan “abhorrent.” Former New York Gov. George Pataki tweeted that the “idea for a Muslim registry is as revolting as it is un-American.”

Ben Carson, meanwhile, reacted to Trump’s comments by saying: "I think we should have a database on everybody ... hopefully we have a database on citizens here."

He then clarified that, “I don't think it's a good idea to treat anybody differently or pick people out based on religion or race."

The notion of a Muslim database also faced ridicule from a constitutional standpoint.

“There are unconstitutional ideas, and then there are ideas that are so patently unconstitutional that they really ought not to even merit a response,” Stephen I. Vladeck, law professor with the American University Washington College of Law, told FoxNews.com.

The Council on American-Islamic Relations also issued a statement condemning Trump for "Islamophobic and unconstitutional" comments.