Trump suggested the two sides were again speaking after an abrupt silence from North Korea prompted US officials to worry. White House aides were not halting some of the summit's planning, which was already underway in Singapore.

And in a tweet on Friday evening, Trump said the US is "having very productive talks with North Korea" about reinstating the summit, likely on the same date.

"We are having very productive talks with North Korea about reinstating the Summit which, if it does happen, will likely remain in Singapore on the same date, June 12th., and, if necessary, will be extended beyond that date," Trump wrote.

It was a sign the President hasn't lost hope in the audacious foreign policy accomplishment he is eager to secure. Even as his aides express doubt the summit can be arranged in the next 18 days, Trump has told confidants and advisers he believes the original date may still hold. And he's grasped at glimmers of hope, in this case a conciliatory statement from Pyongyang that expressed continued openness to talks.

"It was a very nice statement they put out," Trump said on the South Lawn before departing in his helicopter for the US Naval Academy in Maryland, where he was delivering a commencement address. "We'll see what happens. It could even be the 12th. We're talking to them now."

"They very much want to do it," he continued. "We'd like to do it."

While far from a sure thing, Trump's remarks reflect new openness to reviving the talks, or at least rescheduling them. In his letter and during remarks on Thursday, Trump made clear the summit was off. But in conversations Thursday afternoon and Friday morning, Trump did not rule out restoring the meeting, according to people familiar with the conversations.

A planned trip by US officials to survey summit sites, which the White House formally announced on Wednesday, was not canceled, according to a person familiar with the matter. During a briefing with reporters on Thursday, a senior administration official refused to comment on the logistics trip, which is led by deputy chief of staff Joe Hagin.

But the official downplayed the likelihood of the summit proceeding on course.

"The ball is in North Korea's court right now, and there's really not a lot of time. We've lost quite a bit of time that we would need," the official said. "But there's a certain amount of actual dialogue that needs to take place at the working level with your counterparts to ensure that the agenda is clear in the minds of those two leaders when they sit down."

"June 12th," the official said, "is in 10 minutes."

That caution was absent in public remarks from US officials on Friday, including Defense Secretary James Mattis, who told reporters the summit may be "back on."

"We have got some -- possibly some good news on the Korea summit, where it may, if our diplomats can pull it off, may have it back on, even," Mattis said before meeting with his Danish counterpart on Friday. He added that efforts to revive the June 12 summit are now in the hands of diplomats.

"I'll let them talk all they want, and then we'll all hope and pray the diplomats pull it off," he said.

Sarah Sanders, the White House press secretary, told reporters in the White House driveway a June 12 summit was "certainly a possibility."

"The President wants to have a meeting if it can provide real results and that's what he's said all along. It's going to be great for the world and certainly be good for North Korea," Sanders said. "We're always going to be prepared and if the meeting takes place on June 12 we'll be ready. If it takes place on July 12 we'll be ready. We're going to do whatever is necessary to prepare for that on that front."

North Korean reaction

Overnight, North Korea released a statement reiterating its interest in talks, even as it acknowledged the relationship between Washington and Pyongyang had deteriorated.

"We would like to make known to the US side once again that we have the intent to sit with the US side to solve problem(s) regardless of ways at any time," said North Korea's first vice minister of the Ministry of Foreign Affairs, Kim Kye Gwan, in comments published Friday by the country's state-run news agency KCNA.

Kim also said Trump's decision was "not consistent with the desire of humankind for peace and stability in the world, to say nothing of those in the Korean Peninsula."

Trump awoke on Friday and welcomed the warmer language, which stood in sharp contrast to harsh statements over the past week that personally targeted US officials, including Vice President Mike Pence.

Very good news to receive the warm and productive statement from North Korea. We will soon see where it will lead, hopefully to long and enduring prosperity and peace. Only time (and talent) will tell! — Donald J. Trump (@realDonaldTrump) May 25, 2018

"Very good news to receive the warm and productive statement from North Korea," Trump wrote Friday morning on Twitter. "We will soon see where it will lead, hopefully to long and enduring prosperity and peace. Only time (and talent) will tell!"

It wasn't clear on Friday at what level US officials were speaking with their North Korean counterparts, or whether they were discussing the possibility of putting a meeting between Trump and Kim back on the schedule. The White House on Thursday cited a prolonged period of silence as one of the factors in scrapping the June 12 date.

"We got a lot of dial tones," said Secretary of State Mike Pompeo on Capitol Hill.

Another US official told reporters that North Korean officials failed to show up to a planned meeting with US aides to discuss the summit's logistics.

"The North Koreans didn't tell us anything, they simply stood us up," the official said.

Political waves

After news the summit was called off, some Democrats criticized Trump for the decision.

House Minority Leader Nancy Pelosi told reporters Thursday on Capitol Hill that the canceled summit was "a good thing for Kim Jong Un."

Pelosi said the meeting "takes knowledge, this takes judgment and clearly it takes preparation, which the President didn't make."

"It's clear he didn't know what he was getting into," the California Democrat said. "And now he's walking away from it in this very chummy, palsy-walsy letter to Kim Jong Un. He, Kim Jong Un, is the big winner."

Trump on Friday claimed Democrats were "rooting" against his administration in its negotiations with North Korea.

"Democrats are so obviously rooting against us in our negotiations with North Korea," the President wrote on Twitter. "Just like they are coming to the defense of MS 13 thugs, saying that they are individuals & must be nurtured, or asking to end your big Tax Cuts & raise your taxes instead. Dems have lost touch!"

Democrats are so obviously rooting against us in our negotiations with North Korea. Just like they are coming to the defense of MS 13 thugs, saying that they are individuals & must be nurtured, or asking to end your big Tax Cuts & raise your taxes instead. Dems have lost touch! — Donald J. Trump (@realDonaldTrump) May 25, 2018

On a White House-led conference call with political surrogates on Thursday, officials were "defensive" about the cancellation of the summit, according to a person familiar with the conversation.

"They were a little defensive about suggestions that we got ahead of ourselves on the summit," the person said, who described the administration's representatives on the call "genuinely hopeful" the summit would eventually happen.

Asked on Friday whether the North Koreans were playing him, Trump acknowledged they were -- and suggested he was, too.

"Everybody plays games. You know that," he told reporters when asked about the ongoing talks. "You know that better than anybody."