Pompeo: US hopes for 'major' North Korea nuclear disarmament by 2020

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North Korea's leader Kim Jong Un and US President Donald Trump after taking part in a signing ceremony at the end of their historic US-North Korea summit, at the Capella Hotel on Sentosa island in Singapore.

Trump, who said this week that North Korea's nuclear program is "very substantial, " has also softened his rhetoric - suspending military exercises and scaling back his demands for what North Korea must do to receive relief from sanctions.

Joseph Essertier: I think it's good to see there's a dialogue going on now between the governments of the USA and North Korea but unfortunately there is still little dialogue on a grassroots level between Americans and North Koreans because the country is in a state of war and has been continuously since the 1930's. "He was not leaving the summit without claiming he made a deal", Kimmel said.

"The United States is our ally, so the joint military drills are still necessary to maintain our relationship with the US", said Lee Jae Sung, from Incheon. Nor has there been any mention of human rights in the early discussions about follow-up meetings between the Trump administration and the North Korean regime. "But as an example, if Vladimir Putin were sitting next to me at a table instead of one of the others, and we were having dinner the other night in Canada, I could say 'Would you do me a favor?"

Pompeo also said Trump had been "unambiguous" in his conversations with Kim regarding the suspension of joint U.S.

Adam Schiff, a top US Democrat and staunch Trump critic, warned the standoff was far from resolved.

But he said that was no longer the case, and everyone can "sleep well tonight".

Jimmy Kimmel opened his "Jimmy Kimmel Live!" monologue on Tuesday night by laying into President Trump over his summit with North Korean leader Kim Jong Un.

Despite the uncertainties, Trump talked up the outcome of what was the first meeting between a US and North Korean leader in six decades of hostility.

WATCH: Was the North Korea summit a success or a fail?

Japan's Prime Minister Shinzo Abe spoke to Donald Trump after the summit, saying there was "great meaning in Chairman Kim's clearly confirming to President Trump the complete denuclearisation".

"The President's comments [were] very positive and the Statement touches on a new relationship with North Korea, and end to the Korean War, complete denuclearization of the Korean Peninsula and recovering POW/MIA remains - all positive commitments", he said.

He said Trump and Kim reached understandings not written in the document they signed.

"I looked at the document and I said, 'Is this for real?'" he said.

"Kim Jong Un has proved to be a pretty ruthless leader in North Korea, and I'm not sure this sort of speed dating of a 45-minute one-on-one meeting. would suggest that there's nothing to be concerned about", he said. -South Korean drills was met with concern.

"I brought it up absolutely and they are going to be working on that", Trump said.

Wolf Blitzer took a moment of his show today to say that whatever Donald Trump thinks, the media is not the "enemy" of the American people. The next military exercise is scheduled for August, and in years past, has drawn thousands of troops from the U.S., South Korea and other countries.

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