President Donald Trump talked about North Korean real estate opportunities and touched on nuclear physics during a rambling news conference following his summit with Kim Jong-un.

The U.S. president and the North Korean leader signed a four-point agreement in Singapore that called for the lifting of sanctions before the "complete denuclearization" of the Korean Peninsula was verified, and Trump agreed to halt military drills with South Korea.

Both nations also agreed to establish new relations intended to work toward peace, although the terms were vague, and to bring home the remains of American troops killed during the Korean War.

Trump admitted during the post-summit news conference that he would consider lifting sanctions "quickly" and removing U.S. troops from the Korean Peninsula -- two main objectives for Kim -- long before North Korea could prove it had denuclearized.

"You know, scientifically, I've been watching and reading a lot about this, and it does take a long time to pull off complete denuclearization," Trump said. "It takes a long time scientifically, you have to wait certain periods of time, and a lot of things happen. But despite that, once you start the process, it means it's pretty much over. You can't use them. That's the good news, and that's going to start very soon, I believe that's going to start very soon. We will do it as fast as it mechanically and physically can be done."

The president also told reporters that he encouraged Kim to develop his country's "great" beachfront real estate, which Trump said caught his eye in videos of North Korean missile testing.

In off-hand remarks delivered to a press conference in Singapore on Tuesday, Mr Trump said North Korea had great potential for condos and hotels. He also said that from watching coverage of North Korean military drills, it appeared the country boasted “great” beaches.

“Instead of [testing missiles] you could have the best hotels in the world right there,” Trump said he told Kim. “Think of it from a real estate perspective. You have South Korea, you have China and they own the land in the middle."

Trump said he trusts Kim, but admits that time may prove his faith is misplaced.

"I may be wrong, I mean, I may stand before you in six months and say, 'Hey I was wrong,'" Trump said. "I don't know that I'll ever admit that, but I'll find some kind of an excuse."