Trump says 'very productive' dialogue with North Korea is underway, hints Singapore meeting may still happen

• President Donald Trump says his administration has restarted talks with North Korea.
• On Thursday, he cancelled a historic planned summit with the country's dictator Kim Jong Un.
• The president says the June 12 summit in Singapore "could" still happen.

President Donald Trump said Friday that his administration has restarted dialogue with North Korea following his cancellation of a historic summit, with the president suggesting that a meeting between the two countries could even take place on the originally scheduled date.

After days of fiery remarks from North Korea that appeared to suggest the country would not give up its nuclear arsenal, Trump abruptly cancelled the summit in a letter released on Thursday. The cancellation took South Korea by surprise, and left officials in Seoul scrambling to contain the fallout.

However, Trump left the door open to a meeting in the future, and on Friday hinted that the lines of communication remained open.

"We'll see what happens. We're talking to them now," he told reporters as he left the White House on his way to speak at the U.S. Naval Academy graduation.The president added that the scrapped meeting with North Korean dictator Kim Jong Un "could" still happen.

Late Friday, Trump said the two sides were engaged in "very productive" discussions, and a Singapore rapprochement might still be in the cards.

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The summit, part of a process the U.S. hopes will lead to Pyongyang abandoning its nuclear and missile programs, had been set for June 12 in Singapore. If, as Trump suggests, the confab takes place, it will be the first time a U.S. president met with a North Korean leader.

On Thursday, Trump denounced North Korea's "tremendous anger and open hostility." A senior White House official said North Korea had stopped direct communication with the U.S. over the previous week.

Carlos Barria | Reuters

President Donald Trump leaves the White House for a trip to Annapolis, Maryland, in Washington, May 25, 2018.

In a statement issued Thursday evening in response to the summit cancellation, North Korean official Kim Kye-gwan said Pyongyang is "willing to give the U.S. time and opportunities" to reconsider negotiations "at any time, at any format." Kim added that "we remain unchanged in our willingness to do everything we can for the peace and stability of the Korean Peninsula and of the humanity."

On Friday morning, Trump tweeted that it was "very good news" to receive a "warm and productive" statement from North Korea in which the regime indicated its willingness to reconsider talks.

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Separately Friday, Defense Secretary James Mattis told reporters the Trump administration got some "possibly" good news on North Korea, according to Reuters. He said a summit could still take place.

Trump's remarks Friday marked a sharp turn from the aggressive tone the president took Thursday following his decision to cancel the summit. Trump said a "greatly enhanced" U.S. military "is ready if necessary" should North Korea take "foolish or reckless" action.

However, Trump also stressed that he wants a peaceful resolution and was still open to talks. He said "nobody should be anxious" despite the cancellation of the talks designed to head off North Korea's development of nuclear weapons.

"If and when Kim Jong Un chooses to engage in constructive dialogue and actions, I am waiting. In the meantime, our very strong sanctions, by far the strongest sanctions ever imposed, and maximum pressure campaign will continue as it has been continuing," Trump said.

The U.S. and its international allies such as South Korea and Japan have tried to isolate North Korea economically to force Kim to abandon his nuclear ambitions. Reports Thursday indicated the Trump administration could consider new sanctions after the summit fell apart.

Speaking in St. Petersburg on Friday, Japanese Prime Minister Shinzo Abe said the world should keep pushing for a U.S.-North Korea summit to take place. The Japanese leader said he wants to see concrete steps toward North Korea dismantling its weapons program.

The latest escalation between Washington and Pyongyang came this week, when Vice President Mike Pence warned that the North Korean regime may end up like former Libyan leader Moammar Gadhafi. His government was toppled years after he agreed to give up his budding nuclear weapons program.

Choe Son Hui, a North Korean official, responded by calling Pence's remarks "ignorant and stupid."

Trump's move to cancel the summit apparently surprised American allies, including South Korean President Moon Jae-in. Moon played a major role in negotiating the cancelled meeting.

--CNBC's Javier E. David contributed to this article.

WATCH: Summit with N. Korea could still happen