President Trump meets Kim Jong Un
North Korean leader Kim Jong Un did not answer when asked whether he would give up his nuclear weapons.
However, President Trump predicted he would work with Kim to resolve differences over North Korea's nuclear program.
"Working together we’ll get it taken care of," Trump said at the start of an expanded meeting. He said the two leaders "will solve a big problem, a big dilemma."
Kim and President Trump have begun their second rounds of talks, which will end with a working lunch.
President Trump and Kim Jong Un have begun their second series of talks after their personal one-on-one meeting concluded this morning.
Trump, sitting alongside Secretary of State Mike Pompeo, national security adviser John Bolton, White House chief of staff John Kelly and an interpreter told North Korean leader Kim Jong Un that he believes "we will be successful."
"We will be successful," Trump told Kim, sitting directly across from him. "And I look forward to working on it with you. It will be done."
Kim also offered brief remarks through an interpreter.
The extended talks are due to end at 11:30 a.m. local time (11:30 p.m. ET) with a working lunch.
President Trump and North Korea's Kim Jong Un have stepped out of their one-on-one talks to take a walk around the Capella Hotel, where the summit is being held.
After leaving the first session of their summit, Trump told waiting reporters the meeting had been "very, very good."
"Excellent relationship," he said from the balcony of the Capella Hotel.
They were in their personal meeting for about 35 minutes, and are due to start further meetings with advisers at 10 a.m. local time (10 p.m. ET).
Kim has taken a lot of private walks with world leaders since he stepped onto the world stage earlier this year.
In April, Kim went with South Korean President Moon Jae-in for a long stroll around the demilitarized zone, which divides the two countries.
Former NBA star Dennis Rodman told CNN that Tuesday's historic meeting with North Korean leader Kim Jong Un and President Trump was years in the making.
In an emotional interview, Rodman said he always believed in helping North Korea. He said he was even threatened for defending North Korea.
"It's a great day. I am here to see it. I'm so happy," he said. Rodman said he tried talking to former President Obama. "And Obama did not give me the time of day," he said.
Watch the interview:
President Trump and Kim held their first handshake for a dozen seconds as they exchanged a few inaudible words before a display of American and North Korean flags. It was just the beginning of a warm exchange of body language between the two men.
Trump briefly grabbed Kim's upper arm at the beginning of their handshake and then put his arm on Kim's back to guide them to their meeting room.
They then spoke briefly in a corridor before entering their meeting room and both men were smiling as they shook hands again with just two interpreters at their sides.
Trump patted Kim on the back at several points as they made their way along a colonnade to a room for their first meeting.
Trump also offered Kim a thumbs' up after Kim said "we overcame all" of the obstacles that stood in their way.
The interpreter with President Trump is Dr. Yun-hyang Lee, according to a source source familiar.
She’s the division chief of interpreting services at the State Department.
President Trump and North Korea's Kim Jong Un are now meeting one-on-one, the first time a sitting US president has sat down for talks with a North Korean leader.
They are expected to speak alone for another 40 minutes, before other advisers join them for expanded talks at 10 a.m. local time (10 p.m. ET).
The two men will then hold a working lunch, beginning at 11.30 a.m. local time, before the summit ends in the afternoon.
No time has been announced for when the talks might conclude.
President Trump is expected to speak to reporters at 4 p.m. local time (4 a.m. ET), when we're likely to hear what has been accomplished during the day.
Air Force One will then depart Singapore in the early evening, at about 7 p.m. local time.
Speaking to reporters after their first handshake, President Trump and North Korea's Kim Jong Un expressed optimism that the summit would be a success.
What Trump said: The President expressed hope that the historic summit would be "tremendously successful." Sitting next to the North Korean leader, Trump said, "We will have a terrific relationship ahead."
What Kim said: The North Korean dictator said there were a number of "obstacles" to the meeting taking place in Singapore today. "We overcame all of them and we are here today," he told reporters through a translator.
President Trump and Kim Jong Un have headed in for their first face-to-face talks on Tuesday, joined only by two translators.
They'll meet one-on-one for just under an hour, before expanded talks begin at 10 a.m. local time (10 p.m. ET).
On the agenda are North Korea's nuclear capabilities. Trump is hoping he can convince Kim to give up his weapons.
It is the meeting which the Trump has teased could happen for years. In May 2016, during his campaign, Trump said he would be willing to sit down with Kim.
"I would speak to him, I would have no problem speaking to him," Trump said at the time.