President Donald Trump and North Korean leader Kim Jong Un signed a nuclear agreement Tuesday that is as sweeping as it is vague, with the U.S. commander in chief saying it merely kicks off an “arduous” process to potentially disarm the North.

Trump bemoaned the notion that he and U.S. officials gave up a raft of concessions to Kim even before the two leaders shook hands around 9 a.m. local time in Singapore. But he announced that part of the accord includes the United States ending its joint military exercises with South Korea, which Trump called too “provocative.”

The U.S. president, during a news conference at the summit’s end, contended he extracted from Kim “the big thing,” meaning the youthful North Korean leader’s commitment to “complete denuclearization.”

Trump said the two sides will “probably need another summit” as the follow-on negotiations play out.

He also contended the North took steps before the talks that amounted to concessions, such as the release earlier this spring of three American hostages. Trump said Tuesday’s talks also produced concessions from Kim, including his agreement to recover the remains of U.S. troops killed during the Korean War on what is now North Korean soil; a pledge to stop all missile tests; the closure of his “primary” nuclear test site; and the destruction of a missile engine test site Trump said he secured after text of the agreement was written and the document signed.

But Victor Cha, a senior National Security Council official under President George W. Bush, wrote on Twitter Monday that “no testing does not mean no developing.” But he noted that the upside of a testing freeze is that no launches would avert a “crisis.”

Data, not punditry. As we talk, they don’t test – no crisis. Downside – no testing does not mean no developing https://t.co/5OHsudKegz

— Victor Cha (@VictorDCha) June 11, 2018

Kim left Singapore before Trump addressed reporters, with the U.S. leader saying he expects the dictator will start the tedious process of dismantling his nuclear arms program “very quickly.”

Former national security officials and experts say getting inspectors on the ground to verify Kim is taking steps to do just that will be key to ensuring he is living up to the spirit of the vague document he signed Tuesday. But the details of how such inspections and other verification actions will occur were not included in the Trump-Kim pact; those will be ironed out by teams led by Secretary of State Mike Pompeo and his North Korean counterpart.

“There was no time. I’m here for one day,” Trump said when asked why he did not negotiate those details with Kim.

“I may be wrong,” Trump acknowledged near the end of the news conference. “I may stand before you in six months and say ‘I was wrong.’ I don’t know whether I’d ever admit that. I’ll find some kind of excuse.”

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Ben Rhodes, a deputy national security adviser under former President Barack Obama, tweeted that success or failure of the summit cannot be judged “until and unless North Korea actually submits to the type of international inspections that can verify that they are giving up their nuclear weapons (like the inspections that the Iran Deal put in place…)”.

We won’t know until and unless North Korea actually submits to the type of international inspections that can verify that they are giving up their nuclear weapons (like the inspections that the Iran Deal put in place…) https://t.co/N4Aupsndaf

— Ben Rhodes (@brhodes) June 11, 2018

For the last year, Trump and Kim have traded barbs and threats — even suggesting they would attack the other with nuclear weapons. The U.S. leader also suggested other American military action. He had a decidedly different tone and demeanor on Tuesday, smiling widely alongside Kim and often touching the dictator’s shoulder, elbow and back.

“I don’t want to be threatening,” said the president who has derisively called Kim “Little Rocket Man” and threatened to bring “fire and fury” to the North if it moved forward with its nuclear program.

He called the North Korean leader a “worthy negotiator” and “very talented.”

The more diplomatic tone likely will be noted and welcomed by Trump’s Democratic critics.

Illinois Democratic Sen. Tammy Duckworth on Monday applauded Trump for having “paused the reckless rhetoric” about “fire and fury” and possible U.S. military action.

But, like Cha and Rhodes, she said “any agreement must instead lead to the dismantling of every aspect of north Korea’s nuclear missile program, including the country’s sizable fissile material stockpile,” urging Trump to opt against allowing to Kim to secure commitments about reducing the size of the U.S. military footprint in the region.

On that matter, Trump said removing American forces from South Korea or Japan is “not in the equation” right now — though he did repeat his campaign-trail rhetoric about his desire to one day bring some of them home.

Though the agreement is vague and crucial details must still be negotiated, GOP members likely will hail Trump for a historic victory.

Sen. Roy Blunt, R-Mo., a member of the GOP leadership team, told Roll Call late last week that “something positive has to come out of the first meeting.” The president appears to have cleared that hurdle — at least for now.

Trump contended Kim “wants to get it done” and credited him for taking a “bold step toward a bright new future for his people.” To that end, Kim is seeking relief from tough sanctions and other economic aid he needs to develop his economy; Trump told reporters those sanctions would only come down “when we are sure the nukes are no longer a factor.”

“They’ll come off,” a suddenly conciliatory Trump said. “I actually look forward to taking them off.”

For his part, Kim acknowledged “there will be challenges ahead.”

“We overcame all kinds of skepticism and speculations about this summit and I believe that this is good for the peace,” he said through a translator.

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A Politico-Morning Consult poll released Monday, however, found America’s have doubts. Sixty-seven percent of those surveyed said Kim will not give up his nuclear arsenal.

The next steps will be “vigorous negotiations” with North Korean officials that will be calibrated to implement the agreement as soon as possible, Trump said.

“This isn’t the past. This isn’t another administration that never got it started,” he declared.

The bombastic U.S. president lavished Kim, whom Human Rights Watch and similar organizations say runs one of the most brutal governments on the planet, with praise just days after he lashed out at Canadian Prime Minister Justin Trudeau and other G7 leaders following a testy meeting in Quebec. Members of both parties criticized Trump for being too hard on America’s oldest allies and too lenient on Kim and Russian President Vladimir Putin, whose country Trump wants readmitted to the former G8 after it was kicked out for invading part of Ukraine.

“We are being taken advantage of by virtually every one of those countries,” he said. “Very, very seriously. … Canada does have very big advantages over us in terms of trade deficits. … They don’t take our farm products. … It’s very unfair to our farmers. It’s very unfair to the people of our country.”

Trump addressed a photograph that went viral from the G7 summit in which he is sitting with his arms crossed while French President Emmanuel Macron and German Chancellor Angela Merkel appear agitated as they stood over him. The U.S. president said they were “just talking” in a “very friendly” way while they waited for the final text of a joint communique to arrive.

Still, his prepared remarks at the start of the news conference illustrated the difference in his recent statements about the longtime G-7 allies — with whom he is clearly frustrated — and longtime foe North Korea, with whom he at times seems smitten.

Trump said he and Kim are “prepared to start a new history and start a chapter between our two nations,” adding: “Adversaries can indeed become friends.”

Leaders in Ottawa, Brussels, Paris, London and Mexico City might be wondering if the opposite also is true in the Trump era.