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Trump Says Chances for North Korea Summit Revived     

People pass by a TV screen showing a footage of U.S. President Donald Trump during a news program at the Seoul Railway Station in Seoul, South Korea, May 25, 2018.

South Korea said Saturday it is “carefully watching the developments” between the United States and North Korea, after 24 hours of uncertainty as U.S. President Donald Trump canceled then mused about reinstatement of a historic summit June 12 in Singapore with North Korean leader Kim Jong Un.

“We see it as fortunate that the embers of dialogue between North Korea and the United States weren’t fully extinguished and are coming alive again,” Seoul’s presidential spokesman Kim Eui-kyeom said in a statement.

Striking a more optimistic tone, U.S. President Donald Trump said Friday that the White House is having “very productive talks with North Korea about reinstating the Summit.”

In an evening tweet, Trump said the talks “will likely remain in Singapore on the same date, June 12th., and, if necessary, will be extended beyond that date.”

The newest development came after North Korea said early Friday that it remained willing to meet with Trump despite his decision to scrap plans for the historic meeting in Singapore with leader Kim Jong Un.

Trump canceled the planned talks with Kim on Thursday, blaming recent threatening statements by Pyongyang to pull out of the summit over what it saw as confrontational remarks by U.S. officials.

The North Korean diplomat Kim Kye Gwan said Pyongyang’s recent criticisms had been a reaction to unbridled American rhetoric, and that the current antagonism showed “the urgent necessity” for the summit.

WATCH: Trump Says US-North Korea Talks Could be Back on

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Trump Says US-North Korea Talks Could be Back on

“We have inwardly highly appreciated President Trump for having made the bold decision, which any other U.S. presidents dared not, and made efforts for such a crucial event as the summit,” Kim Kye Gwan's statement said.

In a letter released by the White House on Thursday, Trump said, “I was very much looking forward to being there with you. Sadly, based on the tremendous anger and open hostility displayed in your most recent statement, I feel it is inappropriate at this time to have this long-planned meeting.”

The White House said Trump dictated the letter himself.

President Trump's letter to North Korean leader Kim Jong Un.

According to a senior administration official, other factors also led the president to cancel the summit, including poor communication, broken promises and the North Koreans’ failure to show up for a preparatory meeting in Singapore.

“We simply couldn’t get them to pick up the phone,” a White House senior official told reporters on Thursday.

WATCH: For Trump, There's Always a 'New Deal' on the Horizon

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For Trump, There's Always a 'New Deal' on the Horizon

The last straw, according to the White House, was an insult of U.S. Vice President Mike Pence earlier Thursday in a statement by North Korea's vice foreign minister, Choe Son Hui. She called Pence a “political dummy” and warned — in rhetoric typical of that uttered by Pyongyang — of a nuclear confrontation. In his letter, Trump responded in kind, referencing U.S. nuclear capabilities “so massive and powerful that I pray to God they will never have to be used.”

Trump has emphasized that sanctions and “the maximum pressure campaign will continue” to be applied on North Korea while expressing hope Pyongyang’s leadership would decide to join the community of nations.

South Korean President Moon Jae-in meets with North Korean leader Kim Jong Un at Peace House of the Panmunjom in the Demilitarized Zone, South Korea, April 27, 2018.

Trump’s letter caught allies by surprise. The president did not call South Korean President Moon Jae-in or Japanese Prime Minister Shinzo Abe to inform them of it, White House officials confirmed.

Moon expressed “deep regret” over the summit’s cancelation and urged that direct talks between Washington and Pyongyang be held as soon as possible.

North Korea had threatened to pull out of the unprecedented summit after U.S. officials advocated a so-called Libya model approach, which involved that African country’s total nuclear dismantlement before any concessions were granted.

Jeff Seldin contributed to this report.