WASHINGTON (NYTIMES) - Nearly two years into his presidency and more than six months after his historic meeting with North Korean leader Kim Jong Un, United States President Donald Trump finds himself essentially back where he was at the beginning in achieving the ambitious goal of getting Mr Kim to relinquish his nuclear arsenal.

That was the essential message of Mr Kim's annual New Year's televised speech, where he restated that the lifting of international sanctions must begin before North Korea will give up a single weapon, dismantle a single missile site or stop producing nuclear material.

In fact, the list of recent North Korean demands - that all joint military training between the US and South Korea stop, that US nuclear and military capability within easy reach of the North be withdrawn, and that a peace treaty ending the Korean War be completed - was a clear indicator of how the Singapore summit in June altered the optics of the relationship more than the reality.

"It's fair to say that not much has changed, although we now have more clarity regarding North Korea's bottom line," Mr Evans J.R. Revere, a veteran US diplomat and former president of the Korea Society, wrote in an e-mail.

"Pyongyang refused to accept the United States' definition of 'denuclearisation' in Singapore," he wrote, which in the North's view also includes a drastic pullback of any ability to threaten it with nuclear weapons.

"The two competing visions of denuclearisation have not changed since then."

Mr Trump and Secretary of State Mike Pompeo, who is supposed to turn the President's enthusiasms into diplomatic achievements, dispute such conclusions. They note that the tone of one of the world's fiercest armed standoffs has improved. It has; both leaders say they want to meet again.

In a tweet on Tuesday (Jan 1) night, Mr Trump cited Mr Kim's offers not to produce or proliferate weapons, without mentioning the many caveats. He went on to say that he looked forward "to meeting with Chairman Kim who realises so well that North Korea possesses great economic potential!"

Mr Kim's message, delivered in the style of a fireside chat from what appeared to be his library, had none of the old-style threats of turning Seoul into a "sea of fire" or striking the US with a "nuclear sword of justice".

It was full of olive branches. The toughest Mr Kim got was a warning that "if the US does not keep its promises" and continues "with sanctions and pressure" against North Korea, "then we, too, have no choice but to seek a new path for our country's sovereignty".

Mr Trump, for his part, has never returned to his 2017 warning that any hostile moves by the North would be "met by a fire and fury like the world has never seen". He swung to the other extreme, declaring after Singapore that the nuclear threat from the North was over - a statement even his most loyal aides have not repeated - and that he and one of the world's most notorious dictators "fell in love".

By some measures there has been modest progress. It has been 13 months since the North tested a nuclear weapon or a long-range missile, a change that Mr Trump and Mr Pompeo cite as the first fruits of what some officials now concede will be a long diplomatic push.

Relations between the two Koreas are warming, though there is considerable evidence that Mr Kim sees his outreach to South Korean President Moon Jae-in as a way to split the US from its longtime ally.

But Mr Trump's strategic goal, from the moment he vowed to "solve" the North Korea problem rather than repeat the mistakes of past presidents, has been to end the North Korean nuclear and missile threat, not suspend it in place.

Mr Trump dispatched his first secretary of state, Mr Rex Tillerson, to Seoul in March 2017 to declare that a mere nuclear freeze would not be enough. Back then, Mr Tillerson declared there would be no negotiations, and certainly no lifting of sanctions, until the North's dismantling had begun. A nuclear freeze would essentially enshrine "a comprehensive set of capabilities", he argued.

The decision Mr Trump must make now is whether to backtrack on the objective of zero North Korean nuclear weapons - perhaps not hard for a President who has shown he is not hostage to previous policy positions - even if that means risking acceptance of the North as a nuclear-armed state, as the US has done with Pakistan, India and Israel.

Mr Kim's speech seemed infused with a sense that Mr Trump is now facing that critical choice - one the President has never talked about publicly - at a moment of considerable internal disarray, especially at the Pentagon.

"Kim seems to be saying outright that his patience is running thin at the continued insistence on unilateral disarmament," Professor Vipin Narang, a professor at the Massachusetts Institute of Technology who follows North Korea closely, wrote in an e-mail.

"The stick was the threat to go down a 'new path' if the US doesn't reciprocate."

This may all be a negotiating tactic, just as the US insistence that sanctions stay in place until the North is disarmed is a way of maintaining leverage.

To hard-liners like Mr Trump's national security adviser, Mr John Bolton, who excoriated past administrations for making concessions before disarmament, capitulating to Mr Kim on this issue is anathema.

It was Mr Bolton who opened his tenure by suggesting that the North must follow the "Libya model" of surrendering its nuclear equipment and infrastructure first, as Muammar Gaddafi did in 2003. (To Mr Kim, the Libya model means something very different: North Korea media has periodically noted that eight years later, Gaddafi was bombed by the US and its allies, and ultimately assassinated by Libyan revolutionaries.)

Mr Bolton argued in early December that because North Korea had "not lived up to the commitments so far", Mr Trump "thinks that another summit is likely to be productive". In other words, that the only deal to be made is leader-to-leader, something Mr Kim seemed to suggest in his New Year's speech.

But to those who have viewed Mr Trump's "maximum pressure" as a strategy bound to fail, Mr Kim's offer of a step-by-step approach is the only pathway to success - though maybe a success that constrains, rather than eliminates, the North's nuclear ambitions.

"When zero weapons is not on the table - and it's not - then something less than 100 nuclear weapons seems better than the alternative," said Mr Robert S. Litwak, author of Preventing North Korea's Nuclear Breakout and a scholar at the Wilson Centre in Washington.

Mr Trump seems to have taken the first step in that direction by celebrating the North's voluntary freeze on missile and nuclear testing, which has kept it from solving the last physics problems in delivering a nuclear weapon across the Pacific, able to target American cities.

Oddly, Mr Litwak noted, merely constraining a nuclear capability - rather than eliminating it - was Mr Trump's complaint about the Iran nuclear deal, which he abandoned last year.

Mr Trump had argued that the Iran deal was not a permanent solution and that the US was safer reimposing sanctions rather than sticking with an accord that would allow Iran to resume enriching nuclear material - but not build weapons - in 2030.

Now, facing a North Korean state that already has 20 to 60 such weapons - Iran never had any - Mr Trump must decide whether it is better to constrain the growth, or stick with the position he defended so hotly as a presidential candidate and into his first year in office.

Some advisers around Mr Trump, including some who have left in the past year, believe that the number of weapons means little to the President; he wants to be seen as the man who ended the Korean War. That is why, one former adviser said recently, Mr Trump kept repeating the suggestion that he might win a Nobel Peace Prize.

"The bottom line is that Pyongyang wants to keep its nuclear programme, engage the United States in a process designed to improve relations, reassure the United States that it will not use its nukes or proliferate," Mr Revere noted, and "reap the benefits of better ties with Washington."

"Are these disparate and contradictory goals reconcilable?" he asked. "Probably not."