"We're looking at various countries, including Singapore. And we are also talking about the possibility of the DMZ," Trump said in response to a shouted question at the end of a press conference in the White House Rose Garden. "Peace House, Freedom House, and there's something that I thought was intriguing, and I think that some people maybe don't like the look of that, and some people like it very much."
Trump said that he 'threw out' the idea because of its proximity to North Korea.
"There's something I like about it, because you're there, if things work out, there's a great celebration to be had on the site, not in a third party country. We are looking at the possibility of doing it, in that location. So, we're also looking at other countries including Singapore," Trump said.
Trump -- aware of the optics of his potentially historic meeting with Kim -- teased his preference for Peace House, a modern looking 3-story building built to host talks between North and South Korea, in a tweet on Monday morning. The White House is still finalizing plans for Trump's summit in the coming weeks with North Korea.
"Numerous countries are being considered for the MEETING, but would Peace House/Freedom House, on the Border of North & South Korea, be a more Representative, Important and Lasting site than a third party country?" Trump tweeted. "Just asking!"
"It has the chance to be a big event," Trump added. "We'll see what happens I often say, who knows, maybe a lot of things change. But Kim Jong Un who has been very open, and very straightforward so far. I can only say again so far."
Trump expressed optimism about his summit with Kim happening, but added, "we'll see."
"If it's not a success, I will respectfully leave," Trump said.
Trump has not announced his final decision about whether he will withdraw from the Iran nuclear deal by the quickly-approaching May 12 deadline but balked when asked if pulling out of the deal would send the wrong message to North Korea.
"I think it sends the right message. In seven years, that deal will have expired and Iran is free to go ahead and create nuclear weapons. That is not acceptable," Trump said. "I think if anything, what's happening today and over the last little while and what we've learned has really shown that I've been 100 percent right."
During a news conference with the President of Nigeria Muhammadu Buhari, Trump also talked about immigration and said "there's nothing to apologize for" when it comes to his rhetoric.
"There's no reason to apologize our immigration laws in this country are a total disaster. They're laughed at all over the world, they're laughed at for their stupidity and we have to have strong immigration laws. I think if I apologize, it wouldn't make ten cents worth of difference to them. We have to have strong immigration laws to protect our country," Trump said.
Trump said that he has been monitoring the caravan of migrants from Central America that finally reached the border of the United States and Mexico on Sunday.
"It started out with way over 1,000 people, now it's down to 100. Going all through Mexico. People don't realize what a big country Mexico is. We're working on the border with the worst laws," Trump said.
For the first time of his presidency, Trump welcomed a leader from a sub-Saharan African country. Buhari and Trump said their conversations at the White House centered around combating terrorism, the economic relationship between the two countries, and humanitarian crises.
But the visit has also drawn attention after reported remarks by Trump about immigrants from African countries sparked outrage.
Buhari said he did not bring up Trump's vulgar comments during his visit.
"I'm not sure about the validity or whether that allegation was true or not. The best thing for me is to keep quiet," said Buhari.
"We didn't discuss it," Trump said. "And you do have some countries that are in very bad shape and very tough places to live in. We didn't discuss it, because the president knows me, and he knows where I'm coming from and I appreciate that. We did not discuss it."
During a meeting in the Oval Office, Trump said he was most eager to discuss terrorism with Buhari. Nigeria, the most populous country in Africa with almost 200 million citizens, has been on the front-line of terrorism as they fight Boko Haram jihadists.
"Nigeria was one of the first African nations to join the coalition to defeat ISIS and Nigerian forces are currently leading regional efforts against ISIS in West Africa," Trump said.
"Nigeria is also leading in the fight against another terrorist group, Boko Haram," Trump said. "They kidnap the young girls and young women, many of whom never are seen again. Tough stuff."
The Trump administration agreed to the sale of military planes to Nigeria to aid their fight against terrorism in the region.