The president's optimistic tweet comes after North Korea issued a pessimistic statement over the weekend following Secretary of State Mike Pompeo's third visit to Pyongyang - and his first since the president's summit with Kim Jong Un last month.
"There's no doubt in my mind that it's the Chinese pulling a North Koreans back", Graham said.
North Korea's statement bashed hopes for a quick deal and is sure to fuel growing skepticism in the USA over how serious Kim is about giving up his nuclear arsenal.
In a lengthy statement issued on July 7, shortly after Secretary of State Mike Pompeo's two-day, the communist regime accused the United States of making unilateral "gangster-like demands" and called Washington's stance "regrettable".
It dismissed Trump's unilateral order to suspend joint USA and South Korean war games as a cosmetic and "highly reversible" concession and criticised U.S. negotiators who "never mentioned" the subject of bringing the 1953 Korean War to a formal end with a peace treaty.
"Kim has played Trump like a Stradivarius", writes Boot.
Vipin Narang, an associate professor at the Massachusetts Institute of Technology, said the North Koreans were signaling that they have no plans to give up their nuclear arsenal without major concessions.
"The world will see continued enforcement efforts by the United States in the days and weeks ahead".
Mr Pompeo also sought to dispel suggestions the Trump administration had backed down from demanding the complete, verifiable and irreversible dismantlement of the North's nuclear weapons. The desire for a broader security realignment explains why Kim agreed to "denuclearisation" and not disarmament.
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President Donald Trump addresses the audience during a rally at the Four Seasons Arena at Montana ExpoPark, July 5, 2018, in Great Falls, Mont., in support of Rep. Greg Gianforte, R-Mont., and GOP Senate candidate Matt Rosendale.
He also acknowledged that the road ahead would be hard, but said that North Korea did reaffirm its commitment to denuclearize.
"The administration should press on with talks and expect more stumbling blocks along the way, but it must be careful that nuclear talks aren't held hostage to peace talks".
That appeared to be a reference to Trump's national security adviser John Bolton, a prominent North Korea hawk who has been vilified by Pyongyang in the past.
Hyundai Elevator, the largest shareholder of the operator of Mount Geumgan resort in North Korea, tumbled 12% as of 1:36 p.m.in Seoul, while Namhae Chemical, Hyundai Rotem, and Hyundai Engineering & Construction, fell, as well.
"People are going to make stray comments after meetings", Pompeo said.
In practical terms, Pompeo mentioned only that officials from both sides would meet on July 12 to discuss the repatriation of the remains of some United States soldiers killed during the 1950-1953 Korean War.
"The North is trying to get an upper hand in further negotiations", Yang said. Still, Pompeo dismissed North Korea's accusation.
Speaking privately, U.S. officials suggested the harshly-worded North Korean reaction was a negotiating tactic. "We agreed to the denuclearization of North Korea". "China understands this. The US is looking increasingly isolated".