Our live coverage has ended. Scroll down to read more about the two leaders' meeting.
President Trump said he may attend the opening of the US embassy in Jerusalem, which is set to occur in a matter of weeks.
"I may go. I'm very proud of it," Trump said at a news conference.
"Jerusalem has been a subject that's been promised for many years, as you know, the embassy in Jerusalem. It's been promised for many, many years by presidents. They all make campaign promises and they never had the courage to carry it out. I carried it out. So I may go."
Trump said he'd reduced the cost of the building from a $1 billion project to a smaller renovation that cost only $150,000.
President Donald Trump defended his now former VA nominee Dr. Ronny Jackson, saying the way he was treated is a "disgrace."
Jackson withdrew his nomination to lead the VA yesterday. His nomination was hampered by a flurry of allegations about Jackson's professional conduct.
Here's what Trump thinks about all that:
"Ronny Jackson — admiral, doctor — is one of the finest men that I’ve met over the long period of time. Washington can be a very mean place. You don’t know about that, chancellor. A nasty place. The false accusations that were made about him by Sen. Tester from a great state, I don’t think that state is going to put up with it. These were false accusations about a great man, about a man who has a son who is a top student at Annapolis."
He continued: "To make statements of things that most people said never happened, never even happened, calling him names was, to me, a disgrace, an absolute disgrace."
Dr. Ronny Jackson, Trump's pick to the lead the Veterans Affairs agency, withdrew his nomination following allegations about his conduct.
Today, Trump was asked if he had any other people in mind to fill the position.
He said a lot of people want the job, some of them are "excellent" and others are "very political."
"We have many people that want that job," he said. "We're very proud of the job we've done for the veterans."
President Trump said he believes he is responsible for improving the relationship between North and South Korea.
"I think I have a responsibility. I think other presidents should have done it. I think the responsibility has fallen on the shoulders of the president of the United States. I think I have a responsibility to see if I can do it," he said.
And if I can't do it, it will be a very tough time for a lot of countries and a lot of people. It certainly is something that I hope I can do for the world. This is beyond the United States. This is a world problem and it's something I hope I'm able to do for the world."
President Trump said tUS relations with North Korea have changed "very radically" in recent months, pointing to his previous insult exchanges with North Korean Kim Jong Un.
"We have a very good working relationship. We’re setting up a meeting. Things have changed very radically from a few months ago. You know, the name calling and a lot of other things," Trump said.
Trump said a previous administration should have handled the North Korea situation.
"This should have been handled a long time ago, not now. This should not have been left for me to handle. But we will handle it. We’re handling it well," he said.
President Trump, speaking at a joint press conference, said he will be meeting North Korean leader Kim Jong Un in the coming weeks.
He also praised the South and North Korean leaders for holding its historic summit.
"It’s taken a long time, many, many decades to get here," Trump said. "Let’s see what happens."
He again asserted his administration's goal: "complete denuclearization of the Korean Peninsula."
"We seek a future of peace, prosperity and harmony, unlocking a brighter future not on for the people of Korea but for the people of the world," he said.
"However, in pursuit of that goal, we will not repeat the mistake of past administrations. Maximum pressure will continue until denuclearization occurs. I look forward to our meeting. It should be quite something."
President Trump said he and German Chancellor Angela Merkel discussed Iran in their talks today.
"The Iranian regime fuels violence, bloodshed and chaos all across the Middle East," Trump said at a press conference.
"We must ensure that this murderous regime does not even get close to a nuclear weapon, and that Iran ends its proliferation of dangerous missiles and its support for terrorism. No matter where you go in the Middle East, wherever there's a problem, Iran is right there."
What he didn't say: Trump didn't say if the two leaders had come to any agreements in terms of the Iran nuclear deal.
President Trump is set to hold a press conference with German Chancellor Angela Merkel this afternoon. Here are some questions reporters might ask him:
- At a historic meeting between the leaders of North Korea and South Korea, Kim Jong Un committed to a nuclear-free Korean peninsula. Do you trust Kim's word?
- In the wake of the Korea summit, are there any more details about your planned upcoming meeting with North Korea's leader?
- Now that Ronny Jackson has withdrawn his nomination, who will you pick to be the next head of the VA?
- Newly surfaced emails indicate that Natalia Veselnitskaya, the Russian lawyer who met with Trump campaign associates in 2016, once worked with Russia's chief legal office in an effort to thwart the Justice Department, The New York Times reported on Friday. Does your campaign have any comment?
- Why are you skipping the White House Correspondents' Dinner tomorrow night? (Presidents almost always attend and give a speech, although President Trump did also skip last year.)