Pompeo, who held talks with Kim over the weekend, said "we have a pretty good understanding between our two countries about what the shared objectives are".
The announcement was made at a joint news conference with South Korean Foreign Minister Kang Kyung-wha one day after Pompeo returned from North Korea with three American prisoners.
Mr Pompeo said there would need to be "complete" and "verifiable" denuclearisation that would remove North Korea as a threat to the South, the United States and the rest of the world.
In a tweet Saturday afternoon, Trump thanked the North Koreans for their move to dismantle the underground nuclear test site, calling it "a very smart and gracious gesture".
Japan says North Korea abducted at least 17 Japanese citizens in the 1970s and 1980s to train agents in Japanese culture and language to spy on South Korea.
Since Kim took over as leader, he has rarely left his isolated nation and has only officially ventured away from home this year, with two visits to China, most recently travelling to the northeastern port city of Dalian where he met Xi.
Over the past year, Kim and Trump have added a personal touch to a half-century of global enmity, swapping insults and both openly threatening direct military action.
Some experts believe Kim may try to drag out the process to wait out the Trump administration or seek a deal in which he gives away his intercontinental ballistic missiles but retains some of his shorter-range arsenal in return for a reduced US military presence in the South.
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That was also frowned at by the judge who said it was an abuse of the Senate's powers. The judge, therefore, nullified Omo-Agege's suspension "with immediate effect".
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Singapore and the North have a long history of cooperation - the first law firm and fast food restaurant in Pyongyang were both set up by Singaporeans - even if relations hit a snag past year when Singapore enforced new United Nations sanctions on trade.
Mike Pompeo noted the USA has often in history become good friends with former adversaries.
The pair, he said, talked "about how it is he wishes to proceed and if he's prepared, in exchange for the assurances that we're ready to provide him, if he is prepared to fully denuclearize".
"So, in order to achieve that, it will require a robust verification programme and one that we will undertake with partners around the world, which will achieve that outcome in a way that frankly no agreement before it has ever set forth".
Pompeo stated that every one three worldwide locations - the US, South Korea and North Korea - share the identical imaginative and prescient for way forward for the Korean peninsula.
"He does follow the Western press".
"If we get if we get denuclearization, of course there will be sanctions relief". To the USA, that means the North giving up the nuclear weapons it has already built.
"If we can hold to those three principles, this might work", Rice said at Stanford's Hoover Institution. "It is extremely important for North Korea to normalize diplomatic relations with Japan to walk along the right track as part of worldwide society, while accepting its requirements".