The president appeared to reference North Korea destroying parts of its Punggye-ri nuclear test site as evidence that the country is serious about denuclearization.
South Korean President Moon Jae-in, whose efforts were crucial in bringing Trump and Kim together, said there would be no turning back on an agreement that held out the prospect for lasting peace on the peninsula.
Hayden served as director of the National Security Council during the administration of President George W. Bush and as Central Intelligence Agency chief under President Barack Obama.
Warren visited the region in March and has called on the Trump administration to keep Congress informed on its negotiations with North Korea.
At a news conference wrapping up the summit, Trump told reporters he and Kim "have developed a very special bond". "They're gonna put it together, and I think they're going to end up with a very strong country, and a country which has people-that they're so hard working, so industrious".
Congressional Republicans were more measured in their comments, saying much still needs to be determined about what the two leaders had achieved. There was not even a pledge that either side "shall" take action; just the assertion that North Korea will "commit to working towards" denuclearisation, which it sees as a general, not unilateral, process.More news: Navarro voices regret for harsh words about Canadian leader
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Their signed commitment reaffirms an agreement struck between the leaders of North and South Korea.
As reports emerged that the South Korean government was surprised by the announcement, questions were raised about whether Mattis and other US policymakers had also been caught off guard.
"President Trump has granted a brutal and repressive dictatorship the worldwide legitimacy it has long craved", Senate Democratic Leader Chuck Schumer said.
"North Koreans will be heart-broken by seeing the reality of the South, its development, so, in my opinion, the North's government will gradually open its borders". "But we overcame all of them, and we are here today".