"Everybody plays games," President Donald Trump declared Friday as he suggested the potentially historic North Korean summit he had suddenly called off might be getting back on track.

His sights set on a meeting that has raised hopes for a halt in North Korea's nuclear weapons development, Trump welcomed the North's conciliatory response to his Thursday letter withdrawing from the Singapore summit with Kim Jong Un. Rekindling hopes as quickly as he had doused them, Trump said it was even possible the meeting could take place on the originally planned June 12 date.

"They very much want to do it; we'd like to do it," he said.

Later Friday, Trump tweeted that the two countries were "having very productive talks." He wrote that the summit, "if it does happen, will likely remain in Singapore on the same date."

The sweetening tone was just the latest change in a roller-coaster game of brinkmanship — talks about talks with two unpredictable world leaders trading threats and blandishments. On Thursday, White House officials had noted that Trump had left the door open with a letter to Kim that blamed "tremendous anger and open hostility" by Pyongyang but also urged Kim to call him.

By Friday, North Korea issued a statement saying it was still "willing to give the U.S. time and opportunities" to reconsider talks "at any time, at any format." Trump rapidly tweeted that the statement was "very good news" and told reporters that "we're talking to them now."

Confident in his negotiating skills, Trump views the meeting as a legacy-defining opportunity and has relished the press attention and the speculation about a possible Nobel Peace Prize. He made a quick decision to accept the sit-down in March, over the concerns of many top aides, and has remained committed, even amid rising concerns about the challenges he faces in scoring a positive agreement.

Asked Friday if the North Koreans were playing games with their communications, Trump responded: "Everybody plays games. You know that better than anybody."

While the president did not detail the nature of the new U.S. communication with the North on Friday, Defense Secretary Jim Mattis said at the Pentagon, "The diplomats are still at work on the summit, possibility of a summit, so that is very good news." He characterized the recent back-and-forth as the "usual give and take."

A previously planned trip by White House aides to Singapore this weekend to work on logistics for the trip remained on schedule, said two White House officials, who were not authorized to speak publicly.

Secretary of State Mike Pompeo spoke Friday with a top official from South Korea, whose leaders had appeared to be taken aback when Trump withdrew from the summit. Spokeswoman Heather Nauert said Pompeo and South Korean Foreign Minister Kang Kyung-wha reaffirmed their "shared commitment to the denuclearization of the Korean peninsula" and pledged to coordinate "in all of their efforts to create conditions for dialogue with North Korea."

South Korea's government said in a statement released Saturday that it was relieved about the revived talks for a summit.

The U.S. and North Korea do not have formal diplomatic relations, complicating the task of communicating between the two governments. Under the Trump administration, the CIA, where Pompeo served as director before becoming secretary of state, has taken an unusually prominent role in back-channel negotiations.

Pompeo last year assembled a working group at the CIA called the Korea Mission Center, which gradually assumed the lead role in talks with the North Koreans, and the group's director, a retired senior CIA official with deep experience in the region, became the main U.S. interlocutor with Pyongyang.

The group did not supplant the State Department's traditional mode of communication with the North, which is known as the "New York Channel" and involves U.S. diplomats and their North Korean counterparts posted to the United Nations. But it did play the major role in organizing Pompeo's two trips to Pyongyang, once as CIA director and once as secretary of state.

Trump's comments Friday came after days of mixed messages on the summit.

Trump, in his letter to Kim on Thursday, objected specifically to a statement from a top North Korean Foreign Ministry official. That statement referred to Vice President Mike Pence as a "political dummy" for his comments on the North and said it was up to the Americans whether they would "meet us at a meeting room or encounter us at nuclear-to-nuclear showdown."

Trump then said from the White House that a "maximum pressure campaign" of economic sanctions and diplomatic isolation would continue against North Korea — with which the U.S. is technically still at war — though he added that it was possible the summit could still take place at some point.

A senior White House official said the North had reneged on its promises ahead of the summit, including a pledge to allow international inspectors to monitor its explosive destruction of its nuclear test site. The official spoke on the condition of anonymity to avoid overshadowing Trump's comments Thursday.

Trump's aides had warned that merely agreeing to the summit had provided Kim with long-sought international legitimacy and, if Trump ultimately backed out, he risked fostering the perception that the president was insufficiently committed to diplomatic solutions to the nuclear question.

U.S. defense and intelligence officials have repeatedly assessed the North to be on the threshold of having the capability to strike anywhere in the continental U.S. with a nuclear-tipped missile — a capacity that Trump and other U.S. officials have said they would not tolerate.

Russian President Vladimir Putin chimed in from St. Petersburg, saying that "if you don't behave aggressively and if you don't corner North Korea, the result that we need will be achieved faster than many would think, and at less cost."

Trump, speaking Friday to graduates at the U.S. Naval Academy, did not mention North Korea directly, but he stressed the United States' military might.

He said, "The best way to prevent war is to be fully prepared for war."

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Associated Press writers Matthew Lee and Robert Burns contributed to this report.