Secretary of State Mike Pompeo says the Trump administration will walk away from talks with North Korea if the "right deal" is not on the table for negotiation.
Trump weighed in Tuesday, say there was a "very substantial chance" the planned summit with Kim "won't work out".
South Korea welcomed the latest, albeit belated, development, expressing hope that it could lead to the swift and complete denuclearization of the Korean Peninsula.
"We're continuing to do our work and lay the foundation for a successful meeting", Pompeo told reporters.
"Frankly, it has a chance to be a great, great meeting for North Korea and a great meeting for the world", said President Trump.
South Korean journalists arrive at the Kalma Airport in Wonsan, North Korea, on Wednesday.
Punggye-ri has been the site for all six of the North's nuclear tests, the latest and by far the most powerful in September a year ago, which Pyongyang said was an H-bomb.
"I do think he'd like to see that happen", Trump said.
Reporters from China, Britain, the USA and Russian Federation yesterday flew from Beijing to the North Korean city of Wonsan, from where they will travel for some 20 hours up the east coast by train and bus to the remote test site.
The trek will involve an 11-hour train ride, a four-hour bus journey and then a hike of another hour, a reporter with Russia's RT said on Twitter.
Both parties to the talks are invested in holding the meeting, with Kim seeing an opportunity for worldwide legitimacy and Trump the prospect of securing Korean stability - and perhaps a Nobel Peace Prize.
But the North unexpectedly pulled out of planned peace talks with South Korea last week, objecting to U.S.More news: Uber Refused To Hire Michael Cohen
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The newspaper reiterated harsh criticism against Max Thunder, denouncing the exercise as a practice for a pre-emptive airstrike.
South Korea led efforts to resume dialogue with North Korea and Moon gave enthusiastic accounts of its encounters with Kim, spurring Trump to accept an offer of a first-ever meeting between U.S. and North Korean presidents. He said they had discussed their mutual goals for the talks.
When North Korea announced it would dismantle the Punggy-ri site, it said it would invite media from five countries including South Korea to watch, but it didn't respond to South Korea's notifications of which journalists would attend until Wednesday morning.
Observers will be watching the nuclear test site destruction ceremony closely for any clues to the North's mood.
On Wednesday the Unification Ministry said Pyongyang had now granted them permission.
But there has been increasing pessimism about the meeting after North Korea scrapped the inter-Korean talks and threatened to do the same for the Kim-Trump summit in protest of the South Korea-U.S. military drills and what it calls Washington's push for "one-sided" disarmament.
US officials say preparations are still underway.
The Saturday campaign will bring together Maguire, 30 female activists from 16 foreign countries and about 1,000 South Korean volunteers for a 5.5-kilometer march.
The United States stations 28,500 troops in South Korea, a legacy of the 1950-53 Korean War, which ended in a truce, not a peace treaty.
China said that both the United States and North Korea were still making preparations for the summit and Beijing hoped both sides can "clear away distractions". Also, we look at primary election results in several states.
Pompeo said the North Korean leader "asked for the meeting, the president agreed to meet with him".
Russian Federation has expressed support for the U.S. Others say North Korea has learned all it needs from the nuclear tests conducted there.
Russian Federation announced Wednesday that Foreign Minister Sergei Lavrov will travel to North Korea for a visit on May 31.