Trump proclaims 'there is no longer a nuclear threat' from N. Korea after return from Singapore summit

PHOTO: President Donald Trump holds up a document signed by him and North Koreas leader Kim Jong Un following a signing ceremony during their summit at the Capella Hotel on Sentosa island in Singapore on June 12, 2018.PlaySaul Loeb/AFP/Getty Images
WATCH World reacts to North Korea Summit

President Donald Trump took to Twitter to encourage Americans to "sleep well tonight" upon landing in Washington, D.C. Wednesday morning following the landmark United States-North Korea summit in Singapore.

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Trump also tweeted a few congratulatory comments to Republican candidates running in primary races Tuesday, in addition to taking a victory lap for his summit with Kim Jong Un. The "most dangerous problem" outlined by former President Barack Obama was no longer a threat, he added.

After the whirlwind trip, Trump eagerly boasted, "There is no longer a Nuclear Threat from North Korea."

After wrapping a day full of high-stakes meetings with Kim, Trump called the summit a success for ultimately coming to an agreement with the supreme leader on denuclearizing the Korean Peninsula.

But before he landed back home, both opponents and allies raised concerns about any peace agreement with such a longtime enemy of the United States.

"I read the statement and it's difficult for me to see if something was actually agreed to or not," Sen. Bob Corker, R-Tenn., said, adding that the Trump-Kim agreement is nothing more than a "few sentences on a sheet of paper" that were "very aspirational."

Sen. Marco Rubio, R-Fla., tweeted, "One more thing about KJU. While I know @potus is trying to butter him up to get a good deal, #KJU is NOT a talented guy. He inherited the family business from his dad & grandfather. He is a total weirdo who would not be elected assistant dog catcher in any democracy."

Trump was also criticized for giving too many concessions to North Korea, including failing to acknowledge the human rights crimes alleged against Kim, and pledging to end the "war games," or the joint military exercises conducted with a long-standing ally of the United States, South Korea.

"It is worrisome, very worrisome that this joint statement is so imprecise," Senate Minority Leader Chuck Schumer, D-N.Y., said. "What the US has gained is vague and unverifiable at best. What North Korea has gained is tangible and lasting. We've legitimized a brutal dictator who's starved his own people."

A senior South Korean defense ministry official said Tuesday that the South is trying to determine exactly what President Trump meant when he said that exercises would end.

The brief one-page agreement emerging from the meetings provides a framework for a path toward peace with the secluded authoritarian state, but the United States did not achieve many of the goals outlined by the administration leading into the summit.

During a news conference after negotiations between the two leaders, when asked why "complete, verifiable, irreversible denuclearization" was not secured in the details of the agreement, Trump conceded that there simply was "no time."

"I'm here one day," he said. "We're together for many hours intensively but the process is now going to take place."

A timeline laying out exactly when denuclearization of the Korean Peninsula will happen or how long that will take has yet to be determined.

ABC News' Mariam Khan and Ben Gittleson contributed to this report.