"I actually had a name: NATO, right, and then you have ME -- Middle East. NATOME. I said, what a beautiful name," Trump told reporters, in extensive comments about the issue.

"NATO plus ME," he said.

He said he'd proposed the acronym when he called the alliance's secretary general Jens Stoltenberg on Wednesday to demand that other NATO members do more on Middle Eastern security.

"I think he was actually excited by it," Trump said.

"I'm good at names, right?" Trump said, recounting his pride over the new US-Mexico-Canada free trade agreement, known as USMCA, which replaces the former version dubbed NAFTA.

"USMCA, like the song YMCA," Trump said, referring to the 1978 disco hit by the group Village People.

"Nobody could remember USMCA. I said, 'Think of the song YMCA' and now everybody says it."

Little other detail has emerged as to how NATO, a 70-year-old group relying largely on American leadership and firepower, might replace the US in Iraq or other Middle Eastern conflict zones.

Trump said when that happens, "we can come home, or largely come home, and use NATO. This is an international problem."