Washington (CNN) President Donald Trump declared Wednesday that the North Korean regime no longer poses a nuclear threat following his summit with Kim Jong Un, even though the meeting produced no verifiable proof that the rogue regime will discontinue its nuclear program.

In a series of tweets, Trump sought to take political credit for the summit but risked undermining the US strategy in the region.

"Just landed - a long trip, but everybody can now feel much safer than the day I took office," Trump tweeted as he arrived back in Washington. "There is no longer a Nuclear Threat from North Korea."

Trump also said that his meeting with Kim was an "interesting and very positive experience" and that "North Korea has great potential for the future!"

Trump also said in a separate tweet that North Korea is "no longer" the US' "biggest and most dangerous problem," telling Americans and the rest of the world they can "sleep well tonight!"

After returning to the White House Wednesday, Trump also defended his decision to halt the joint military exercises with South Korea, which he called "war games" -- a term used by Pyongyang -- arguing on Twitter that the US will "save a fortune."

Before taking office people were assuming that we were going to War with North Korea. President Obama said that North Korea was our biggest and most dangerous problem. No longer - sleep well tonight! — Donald J. Trump (@realDonaldTrump) June 13, 2018

Trump's tweets pointed to one of the chief gains at the summit from the US point of view -- that its scheduling and the establishing of a relationship between the President and Kim have eased fears that the two sides are on a slide toward a disastrous war.

The argument also allows Trump's political allies and supporters in conservative media to claim ahead of the midterm elections that the President has engineered a triumph overseas that was beyond all his predecessors and has made America and the world much safer.

No guarantees from summit

After nearly five hours of unprecedented talks between Trump and Kim on Tuesday, the two leaders signed a document in which Kim "reaffirmed his firm and unwavering commitment to complete denuclearization of the Korean Peninsula" and the US agreed to "provide security guarantees."

However, there was no mention of the previous US aim of "complete, verifiable and irreversible denuclearization" from Pyongyang. Kim's commitments did not appear to go beyond what he already pledged to do in April when he met with South Korean President Moon Jae-in along their countries' border.

Following the summit, Trump told reporters during a news conference in Singapore that Kim agreed to "destroying a major missile engine testing site" and that it would be done "very soon," without elaborating further on which testing site or timing.

The President also added that North Korea's promise to complete denuclearization "will be verified," though the document the two leaders signed did not lay out details of that process.

Trump left the discussions assured that Kim would begin dismantling his country's missile sites in the immediate future, telling ABC News that Kim " trusts me, and I trust him ."

Risk of weakening US position

Any lessening of tensions is positive but an assurance that the threat of war is removed based simply on a relationship between a President who is term-limited and a volatile dictator who leads a criminal regime lacks the certainty and permanence of verifiable disarmament that the administration says is its goal.

By claiming that the North Korean nuclear threat has disappeared, Trump also risks weakening the US negotiating position in talks on denuclearization that were mandated by the summit and will be led from the US side by Secretary of State Mike Pompeo. After all, if there is no threat, why would the North Koreans need to give up their arsenal?

Trump's rush to claim credit for the supposed disappearance of the North Korean nuclear threat may also give nations like China and Russia an incentive to ease stringent implementation of the "maximum pressure" sanctions that helped bring Pyongyang to the table.

Some analysts are likely to see the comments as part of a worrying trend since North Korea showed no public sign at the summit or since that it is now willing to implement the complete, irreversible and verifiable destruction of its nuclear programs. Ultimately, in the short term, at least while diplomacy continues, Trump's tweets seem to indicate he is ready to live with the fact that North Korea has nuclear weapons and potentially the capacity to fire them at the United States, in an implicit erosion of the US strategic position.

Ultimately, that may end up being the only option that the US has short of war. But Trump's triumphalism is not based on concrete commitments by Kim that were established by his own administration's expectations setting before the talks.