PYONGYANG, North Korea >> The leaders of North and South Korea announced a wide range of agreements today which they said were a major step toward peace on the Korean Peninsula. But the premier pledge on denuclearization contained a big condition, with North Korean leader Kim Jong Un stating he’d permanently dismantle his main nuclear complex only if the United States takes corresponding measures.

Compared to the vague language of their two summits earlier this year, Kim and South Korean President Moon Jae-in agreed in their second day of meetings to an ambitious program meant to tackle soaring tensions last year that had many fearing war as the North tested a string of increasingly powerful weapons.

Kim promised to accept international inspectors to monitor the closing of a key missile test site and launch pad and to visit Seoul soon, and both leaders vowed to work together to try to host the Summer Olympics in 2032.

But while containing several tantalizing offers, their joint statement appeared to fall short of the major steps many in Washington have been looking for — such as a commitment by Kim to provide a list of North Korea’s nuclear facilities, a solid step-by-step timeline for closing them down, or an agreement to allow international inspectors to assess progress or discover violations.

The question is whether it will be enough for President Donald Trump to pick up where Moon has left off. Trump, tweeting about the Korean leaders’ agreements, said, “Very exciting!”

Declaring they had made a major step toward peace, Moon and Kim stood side by side as they announced the joint statement to a group of North and South Korean reporters after a closed-door meeting Wednesday morning. They took no questions.

“We have agreed to make the Korean Peninsula a land of peace that is free from nuclear weapons and nuclear threat,” Kim said at the guesthouse where Moon is staying. “The road to our future will not always be smooth and we may face challenges and trials we can’t anticipate. But we aren’t afraid of headwinds because our strength will grow as we overcome each trial based on the strength of our nation.”

Kim and Moon earlier smiled and chatted as they walked down a hallway and into a meeting room to finalize the joint statement, which also said that the leaders would push for a Korean Peninsula without nuclear weapons and to “eliminate all the danger of war.” Moon and Kim planned to visit a volcano sacred to the North on Thursday, the last day of Moon’s visit.

This week’s summit comes as Moon is under increasing pressure from Washington to find a path forward in efforts to get Kim to completely — and unilaterally — abandon his nuclear arsenal.

Trump has maintained that he and Kim have a solid relationship, and both leaders have expressed interest in a follow-up summit to their meeting in June in Singapore. North Korea has been demanding a declaration formally ending the Korean War, which was stopped in 1953 by a cease-fire, but neither leader mentioned it Wednesday as they read the joint statement.

In the meantime, however, Moon and Kim made concrete moves of their own to reduce tensions on their border.

According to a statement signed by the countries’ defense chiefs, the two Koreas agreed to establish buffer zones along their land and sea borders to reduce military tensions and prevent accidental clashes. They also agreed to withdraw 11 guard posts from the Demilitarized Zone by December and to establish a no-fly zone above the military demarcation line that bisects the two Koreas that will apply to planes, helicopters and drones.

Though not directly linked to security, the leaders’ announcement that they would seek a joint Summer Olympics was a significant move in terms of easing tensions and building trust. It also flows from the North’s decision to participate in the Pyeongchang Winter Games in February, which was regarded as a success for both sides.

Other agreements aimed at removing some longstanding irritants from their relations, such as allowing more contact between families divided by the Korean War. Moon also appeared to be making good on his proposals to help build up the North’s infrastructure and open cross-border rail links.

Unlike Trump’s initial tweets praising the summit, the news brought a quick and negative response from Republican Sen. Lindsey Graham, who tweeted that he was concerned the visit would undermine efforts by Secretary of State Mike Pompeo and U.N. Ambassador Nikki Haley to impose “maximum pressure” on the North.

“While North Korea has stopped testing missiles and nuclear devices, they have NOT moved toward denuclearization,” he tweeted.

With the main business of the day complete, North Korea was expected to hold a huge mass games spectacle in the evening, with Moon as the special guest. Seoul said Moon would make a short speech.

North Korea had put the iconic games, which feature tens of thousands of performers dancing and flipping placards in unison to create giant mosaics and slogans, on a back burner for the past several years, but revived them for this month’s celebrations of its 70th founding anniversary. In a performance for the anniversary, a giant photo of Moon and Kim shaking hands at their first summit in April was projected onto one side of the stands in Pyongyang’s 150,000-seat May Day Stadium.

Kim has gone all out to make Moon’s visit a memorable one.

On Tuesday, the first day of the summit, he greeted Moon and his wife at Pyongyang’s airport and then rode into town with Moon in an open limousine through streets lined with crowds of North Koreans, who cheered and waved the flag of their country and a blue-and-white flag that symbolizes Korean unity.

At the start of their meeting, Kim thanked Moon for brokering the June summit with Trump.

“It’s not too much to say that it’s Moon’s efforts that arranged a historic North Korea-U.S. summit. Because of that, the regional political situation has been stabilized and more progress on North Korea-U.S. ties is expected,” Kim said, according to South Korean media pool reports and Moon’s office.