WASHINGTON (Reuters) - U.S. President Donald Trump said on Monday the demilitarized zone between North and South Korea would be an excellent venue for his planned summit with North Korean leader Kim Jong Un but that Singapore was also a possible site.

Trump’s comments at a news conference with visiting Nigerian President Muhammadu Buhari suggested the Peace House on the DMZ, where Kim met South Korean President Moon Jae-in last week, was the likely setting for the first-ever meeting between sitting leaders of the United States and North Korea.

But a senior U.S. official said Singapore was still high on the list of potential sites for the summit, whose date still remains to be established. Trump wants to hold it by late May or early June.

“We’re looking at various countries, including Singapore. And we are also talking about the possibility of the DMZ Peace House/Freedom House,” Trump said.

Trump said the Peace House carried symbolic value that having the summit in a third country would not have. The president tried to visit the DMZ last November during a trip to Seoul, but dense fog forced his helicopter to turn back.

Some U.S. officials have argued privately that having the summit in the demilitarized zone between the two Koreas would present the unwelcome appearance of Trump traveling to Kim instead of the two of them meeting at a neutral site.

But officials have also debated how far Kim would be able to travel.

“I think that some people maybe don’t like the look of that,” Trump said of the idea of a DMZ summit. “And some people like it very much.”

He said he had raised the idea with Moon, days after dramatic images of Moon meeting Kim at the Peace House dominated the news.

“There’s something that I like about it because you’re there,” he said. “You’re actually there, where if things work out, there’s a great celebration to be had on the site.”

Buoying prospects for the Trump-Kim summit was a North Korean announcement on Sunday that it would close its main nuclear test site next month.

But many U.S. officials are doubtful that Kim will actually agree to give up nuclear weapons after working so long to develop them.

Trump said the North Korean decision to close the test site, along with its suspensions of nuclear and ballistic missile tests, were hopeful signs.

But he said North Korea had “to get rid of the nuclear weapons” for peace efforts to be a success.

Trump, who has declined to comment on whether he has spoken directly to the North Korean leader, called Kim “very open and very straightforward so far.”

“Oh yeah, I think the summit’s going to happen,” he said. They very much want it. We certainly would like to see it. ... I will say this: If it’s not a success. ... I will respectfully leave. It’s very simple.”