"Kim Jong Un has agreed to allow nuclear inspections, subject to final negotiations, and to permanently dismantle a test site and launch pad in the presence of global experts", Trump said on Twitter, referring to agreements the North Korean leader made in talks with South Korea's President Moon Jae-in.
"The North agreed to permanently close the Tongchang-ri missile engine test site and missile launch facility in the presence of experts from relevant nations", Mr Moon said after the signing.
The agreement came in a historic summit between Kim and South Korean President Moon Jae-in held at the state guesthouse Paekhwawon in Pyongyang.
Although Trump has remained optimistic about improved relations between Washington and Pyongyang, the initial euphoria following the Singapore summit in June - after which the president declared that North Korea was "no longer a nuclear threat" - quickly wore off.
North Korea's May Day Stadium is the largest in the world with a reported capacity of 150,000.
Moon said: "The seeds to a peaceful future have been planted". But experts said the document only contained vague promises that would do little to curb the North's nuclear program.
It was not clear what Trump meant by nuclear inspections.
Ahead of the trip, Mr Moon said he was pushing for "irreversible, permanent peace" and for better dialogue between Pyongyang and Washington.
Kim made the announcement during a three-day summit with South Korean President Moon Jae-in in Pyongyang that began Tuesday, the third such meeting this year.
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Australian media reported a man in Queensland was hospitalized after swallowing part of a needle and developing abdominal pain. Woolworths have said they have taken the contaminated strawberries off the shelves as the investigation continues.
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Kim's latest promises come days before Moon meets Trump in NY on the sidelines of the U.N. General Assembly next week.
Though North Korea has unilaterally stopped nuclear and missile tests, it did not allow global inspections of the dismantling its only known nuclear test site in May, drawing criticism that its action was for show and could be easily reversed.
US President Donald Trump welcomed developments by North Korea at an inter-Korean summits.
"I think we should take these steps as very positive, but remember that North Korea is still taking baby steps", said Melissa Hanham, a senior research associate at the James Martin Centre for Nonproliferation Studies.
North and South Korea issued a joint statement Wednesday laying out more steps North Korea is prepared to take to denuclearize, but offering few details as to how they will get there.
North Korea has reportedly dismissed the US demand, an apparent source of the ongoing impasse in the US-North Korea denuclearization talks.
In it, defense chiefs from Pyongyang and Seoul said they would establish "buffer zones" between their land and maritime borders to reduce the possibility of accidental military clashes.
North and South Korea will make a joint bid to host the Summer Olympic Games in 2032, the countries have announced after a friendly summit.