SEOUL (Reuters) - A year after President Donald Trump and North Korea’s Kim Jong Un met for the first time, they appear committed to a personal bond upon which hopes for peace seem to rest despite a stalemate in efforts to get Kim to abandon his nuclear weapons.

Trump and Kim agreed at the first U.S.-North Korea summit in Singapore to work toward the complete denuclearization of the Korean peninsula, easing fears of war between their countries.

But there has been little progress since then and tension has again been rising with North Korea resuming some limited testing of weapons and warning of “truly undesired consequences” if the United States was not more flexible.

But Trump said on Tuesday he had received a “beautiful letter” from Kim.

“I can’t show you the letter obviously, but it was a very personal, very warm, very nice letter,” Trump told reporters outside the White House.

Trump, who has tried to convert what he feels is a warm personal relationship with Kim into a diplomatic breakthrough, gave no details, but repeated that he believed North Korea had “tremendous potential”.

“I think that something will happen that’s going to be very positive,” he said.

North Korea’s state media has not mentioned any letter.

The optimism that the two leaders generated in Singapore all but evaporated in February when a second summit, in Vietnam, dramatically fell apart without even a recommitment to the general goals outlined in a statement signed in Singapore.

Since then, North Korea has complained of U.S. sanctions and Kim said he would wait until the end of the year before deciding on whether to take a “new path”.

Both sides have said they are open to talks but that the other side needs to change their policy.

FILE PHOTO: U.S. President Donald Trump shakes hands with North Korean leader Kim Jong Un at the Capella Hotel on Sentosa island in Singapore June 12, 2018. REUTERS/Jonathan Ernst/File Photo

The United States says North Korea needs to make verifiable progress toward giving up its nuclear weapons before any sanctions are eased, while North Korea says the United States has done nothing to reward steps already taken.

In the weeks ahead of Wednesday’s anniversary of the Singapore summit, North Korean state media has repeatedly warned that the statement signed there was in danger of being rendered meaningless if the United States did not drop demands for North Korea to unilaterally dismantle its nuclear arsenal.

According to the Singapore foreign ministry, North Korea’s embassy there had been planning an event to commemorate the summit anniversary and invited Singapore officials. But it later canceled the event.

‘UPS AND DOWNS’

Still, North Korea has said it “remains unchanged in its stand and will to cherish and implement in good faith” the Singapore statement, which included vague promises to improve relations and eventually pursue the denuclearization of the Korean peninsula.

A third summit between Trump and Kim was possible but the ball was in Pyongyang’s court, White House national security adviser John Bolton said on Tuesday.

Bolton said the United States was continuing its “maximum pressure campaign” because Kim still appeared not to have made “a strategic decision to give up the pursuit of deliverable nuclear weapons.”

South Korean President Moon Jae-in on Wednesday expressed hope for an inter-Korean summit before Trump’s planned visit to South Korea in late June, but added “this is up to chairman Kim to decide”.

Moon said Kim and Trump should meet in the near future to maintain the momentum for dialogue.

“If the period of no dialogue is prolonged, the passion for dialogue could subside,” Moon said during a visit to Oslo.

U.S. State Department spokeswoman Morgan Ortagus said on Monday North Korea is “one of the toughest national security challenges”.

“There’s always ups and downs, and we remain confident that Kim Jong Un and his government will see a path for a brighter future for the North Korean people,” she told reporters.

“And one year later, that’s what we are still aspiring to and still hoping for while noting, of course, that economic sanctions do remain.”

Those sanctions remain a key sticking point, with North Korea calling them illegal after the United States announced it had seized a North Korean cargo ship accused of illicit coal shipments in violation of sanctions.

The United States is also keen to secure more sanctions enforcement by China.

Chinese foreign ministry spokesman Geng Shuang said that while negotiations had slowed, North Korea still wanted a denuclearized Korean peninsula and both it and the United States were committed to resolving their issues via talks.

“It is an intricate and complex problem and cannot be solved overnight,” Geng told reporters.

In May, Kim oversaw the test launch of new, short-range missiles while giving a cold shoulder to projects planned with South Korea.

The North’s leader has maintained his efforts to build diplomatic ties with other countries, meeting Russian President Vladimir Putin in April.

Kim sent Putin a congratulatory message on Wednesday saying he believed that “the common understanding and agreements made at our first significant meeting will bear rich fruits”.