"I would certainly implement that. Absolutely," Trump told NBC News
during a campaign stop in Newton, Iowa.
He continued: "There should be a lot of systems, beyond databases. We should have a lot of systems."
Trump, who also said this week that he would consider shutting down mosques, told Yahoo News
earlier Thursday that "we're going to have to look at a lot of things very closely" when asked about a national database for Muslims.
Those answers seemed at odds with a follow-up question from CNN's Sara Murray in Newton. When Murray asked whether Trump would rule out a database for Muslims, he said he didn't "know where you heard that."
"Yahoo News asked you about it, you didn't rule it out," Murray said as Trump worked a ropeline after the event.
"No, I never -- I never responded to that question," Trump said.
"So would you not support it?" Murray asked.
"I never responded to that question, Sara," Trump said.
He added that he didn't "know who wrote it," referring to the Yahoo News article, and declined to answer a follow-up question from Murray about whether he would "support something like that," referring to a Muslim database. He also declined to respond when Murray asked "what's your view of it?" as he continued down the ropeline.
His spokeswoman Katrina Pierson said Friday on Fox Business that Trump "is just saying he won't rule anything out."
"Those are a reporters' words and now everyone is saying it's all Trump. He's simply saying he won't take anything off the table," Pierson said.
When the anchor pressed her, suggesting a religion-based database isn't something that is done in the U.S., Pierson said "we don't do that, but we do have a watch list, a terrorism watch list."
Trump has repeatedly suggested it would be "insane" to allow Syrian refugees into the U.S. for fear that terrorists could infiltrate their ranks and slammed President Barack Obama for his plans to resettle 10,000 Syrian refugees in the United States over the next year.
"I think he's a threat to our country. I mean he must have some kind of a thing going because, you know, when you see that he won't even call them by their name, attack after attack after attack," Trump said Wednesday on Boston's WRKO radio.
"It's radical Islamic terrorism and he won't even acknowledge it -- it's like they're coming out of Denmark or something."
Trump added that Obama "doesn't have any clue" when it comes to defeating ISIS.
The Republican front-runner's attack on the president came after Obama had slammed Republicans' calls to stop admitting any Syrian refugees into the United States as "offensive," "political posturing" and a "potent recruitment tool" for ISIS.
"We are not well served when, in response to a terrorist attack, we descend into fear and panic," Obama said earlier on Wednesday. "We don't make good decisions if it's based on hysteria or an exaggeration of risks."
Trump also slammed Hillary Clinton for not labeling the terrorist threat the U.S. faces as "radical Islam."
But Trump went beyond knocking Clinton for the language she uses in discussing the threat of terrorism, suggesting she lacks the "strength or the stamina" to lead the country.
"She doesn't have the strength, she doesn't have the stamina," Trump said. "Hillary does not have the strength or the stamina to be president, and she doesn't have the ideas."
In a separate interview, Trump knocked ripped Democratic presidential candidate Bernie Sanders as a "communist."
"I think he's a communist. I think he's actually a communist with a socialistic bent," Trump told Yahoo News. "Anybody that would say that the Paris attacks were caused by global warming, there's something missing."
Sanders calls himself a "democratic socialist" and has said that he believes the greatest threat facing the country is global warming, and he linked climate change to unrest in the Middle East in the last Democratic debate.