U. S. President Donald Trump shakes hands with North Korea leader Kim Jong Un at the Capella resort on Sentosa Island Tuesday, June 12, 2018 in Singapore. (Kevin Lim/The Straits Times via AP)

U. S. President Donald Trump shakes hands with North Korea leader Kim Jong Un at the Capella resort on Sentosa Island Tuesday, June 12, 2018 in Singapore. (Kevin Lim/The Straits Times via AP)

SINGAPORE (AP) — The Latest on the summit between North Korean leader Kim Jong Un and President Donald Trump (all times local):

8:20 a.m.

President Donald Trump is thanking North Korean leader Kim Jong Un for “taking the first bold step toward a bright new future for his people,” saying their summit Tuesday “proves that real change is possible!”

Tweeting from Air Force One, which just landed in Hawaii to refuel on the trip back from Singapore, Trump says, “There is no limit to what NoKo can achieve when it gives up its nuclear weapons and embraces commerce & engagement w/ the world.”

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Trump is celebrating Tuesday’s agreement to launch a process to denuclearize the Korean Peninsula, though experts and allies are still awaiting details on the broad accord the two sides say they’ve reached.

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8:15 a.m.

North Korea says leader Kim Jong Un and President Donald Trump have agreed to visit to each other’s country at an unspecified time.

The invitations appear to be a trade of diplomatic pleasantries, and could also depend on progress in denuclearization that Kim promised to Trump during Tuesday’s summit.

Pyongyang’s Korean Central News Agency said Wednesday that Kim invited Trump to visit Pyongyang “at a convenient time.”

It says Trump also invited Kim to visit the United States.

KCNA says the two leaders “gladly accepted each other’s invitation, convinced that it would serve as another important occasion for improved” relations between their countries.

No sitting American and North Korean leaders have visited each other’s countries since the end of the 1950-53 Korean War.

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7:40 a.m.

North Korea says U.S. President Donald Trump expressed his intention during a summit with North Korean leader Kim Jong Un to halt joint military drills between the U.S. and South Korea.

The North’s official Korean Central News Agency said Wednesday that Trump also expressed his intention to offer security guarantees to North Korea and lift sanctions “over a period of good-will dialogue” between the two countries.

KCNA quoted Kim as saying that the North can take unspecified “additional good-will measures of next stage commensurate with them” if the United States takes genuine measures to build trust.

KCNA quotes Kim as saying it’s “urgent to make a bold decision on halting irritating and hostile military actions against each other.”

Annual military drills between the United States and South Korea have been a major source of tension on the Korean Peninsula. The North has called them an invasion rehearsal and responded with its own weapons tests.

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7 a.m.

North Korea says President Donald Trump has agreed on a step-by-step denuclearization process by North Korea in return for reciprocal concessions from the United States during a summit with its leader Kim Jong Un.

The Korean Central News Agency said Wednesday the two leaders “shared recognition to the effect that it is important to abide by the principle of step-by-step and simultaneous action in achieving peace, stability and denuclearization of the Korean Peninsula.”

The reported agreement, if confirmed by the United States, could be considered as a concession by Trump because U.S. officials had called for the North to take swift disarmament measures before getting major outside concessions and benefits.

Some experts say a step-by-step denuclearization process is a ploy to win concessions while delaying disarmament.

Trump and Kim met in Singapore on Tuesday for their countries’ first-ever summit talks.

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3:45 a.m.

Former Vice President Joe Biden says he is troubled by the outcome of the summit between President Donald Trump and North Korean leader Kim Jong Un.

Biden says in a statement released Tuesday that Trump has given North Korea multiple “wins up front without getting anything in return.” He says those include an easing of pressure on Pyongyang, the suspension of U.S.-South Korean military exercises and the summit itself, which gave Kim legitimacy.

Biden says that in return, Trump got only “vague promises” to begin negotiations on North Korea’s nuclear program, reducing U.S. leverage.

Biden is accusing Trump of taking “an inexcusable and irresponsible approach” to the summit by not fully preparing for it, and he is urging the administration to focus on denuclearizing the Korean peninsula.

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1:43 a.m.

The parents of Otto Warmbier, the American college student who died after being released from a North Korean prison last year, are thanking President Donald Trump for his kind words about their son.

Fred and Cindy Warmbier said in a statement Tuesday after Trump met with North Korea’s Kim Jong Un that they appreciated the president’s comments. They said they were hopeful that something positive could come from the summit.

Earlier in Singapore, Trump said that Otto Warmbier was a “very special person” and that his death had galvanized the administration’s determination to deal with North Korea. Trump said Otto Warmbier had not died in vain.

Warmbier was a student at University of Virginia who was arrested by North Korean authorities in January 2016 for stealing a propaganda poster and sentenced to 15 years in prison with hard labor. After suffering still unexplained brain injuries, he was released on June 13, 2017 and died six days later.

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12:48 a.m.

Israel’s prime minister is congratulating President Donald Trump for an “historic” summit with North Korean leader Kim Jong Un.

Benjamin Netanyahu (neh-ten-YAH’-hoo) said in a statement Tuesday that the meeting was an important step toward the denuclearization of the Korean Peninsula.

He also praised Trump’s “tough” stance on Iran and its nuclear program, which he said was already affecting Iran’s economy. He said: “President Trump’s policies are an important tiding for Israel, the region and the entire world.”

Netanyahu has been one of Trump’s most vocal supporters on the global stage. He vehemently opposed the Iran nuclear deal signed between world powers and Iran, from which the U.S. withdrew last month.

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11:55 p.m.

President Donald Trump says North Korean leader Kim Jong Un “loves his people, not that I’m surprised by that, but he loves his people.”

Trump made his comments during an interview with VOA that followed his historic meeting with Kim, looking beyond Kim’s international reputation for having one of the worst human rights records in the world.

Political prisoners in the country number in the tens of thousands and systematic torture and assassinations, including of his own brother, are not unheard of.

In the past, Trump has spoken of the “horror” of life in North Korea and met in February with eight defectors from that country at the White House.

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10:51 p.m.

The Vienna-based body set up to oversee a treaty banning nuclear testing worldwide is welcoming the “positive and direct dialogue” between the U.S. and North Korean leaders and offering to support verification efforts.

Lassina Zerbo is the executive secretary of the Comprehensive Test Ban Treaty Organization. He says he hopes that Tuesday’s summit “will provide a basis for progress toward verifiable denuclearization of the Korean Peninsula.”

Zerbo says his group would, if invited, “support any verification activities for the permanent closure of the Punggye-ri nuclear test site.”

The organization was created more than 20 years ago to monitor the Comprehensive Test Ban Treaty, but that deal has not yet gone into force because key nations have yet to ratify it.

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10:50 p.m.

The U.N. says Secretary-General Antonio Guterres is calling the summit between President Donald Trump and North Korean leader Kim Jong Un “an important milestone” in advancing peace and “complete and verifiable denuclearization on the Korean Peninsula.”

U.N. spokesman Stephane Dujarric says the secretary-general “urges all concerned parties to seize this momentous opportunity.”

Dujarric said Guterres wrote to both leaders before the summit and reiterates Tuesday that “the road ahead requires cooperation, compromise and a common cause.”

Guterres told reporters Monday that the International Atomic Energy Agency and other parts of the U.N. system “stand ready to support this process in any way, including verification if requested by the key parties.”

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10:46 p.m.

Senate Democratic Leader Charles Schumer says President Donald Trump already has given up American leverage over North Korea.

The New York Democrat said Tuesday during a speech on the Senate floor that Trump’s meeting with Kim Jong Un might well have been “a reality show summit.”

Schumer spoke as Trump celebrated the first meeting in history between a sitting U.S. president and a North Korean leader. But Trump also faced mounting questions about whether he got too little and gave away too much — including an agreement to halt U.S. military exercises with treaty ally South Korea.

He said if North Korea does not denuclearize, the “meeting alone will be a victory for North Korea and a defeat for the U.S.”

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10:15 p.m.

Senate Republican Leader Mitch McConnell says President Donald Trump’s meeting with North Korea’s Kim Jong Un produced “a major step” toward peace.

But the Kentucky Republican said that if the North does not follow through with complete denuclearization, “We and our allies must be prepared to restore the policy of maximum pressure.”

McConnell, speaking Tuesday in Washington, was referring to Secretary of State Mike Pompeo’s statement that the U.S. goal remains the “complete verifiable and irreversible denuclearization of the Korean peninsula.” That language is not included in the agreement.

McConnell added that “the next steps in negotiation will test whether we can get to a verifiable deal which enhances the security of North East Asia, our allies and of course, the United States.”

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Follow AP’s summit coverage here: http://apne.ws/MPbJ5Tv