U.S. President Donald Trump and Democratic People's Republic of Korea (DPRK) leader Kim Jong Un have agreed to continue "productive" discussions on denuclearization, Pyongyang's state media said on Friday, hours after the second summit between the two leaders ended abruptly with no agreement in Hanoi. 

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The highly-anticipated meeting in Vietnam was expected to build on their historic first summit in Singapore last year, but the latest talks ended in a deadlock with Washington and Pyongyang giving starkly different accounts of the reasons behind the impasse.

On Friday, however, the DPRK's KCNA news agency said that Kim and Trump had "agreed to continue having productive talks to discuss the denuclearization of the Korean Peninsula and improvement of U.S.-North Korea (DPRK) relations."

"Chairman Kim and President Trump have expressed their confidence that North Korea (DPRK)-U.S. relations can achieve groundbreaking improvements if they collaborate together with patience and wisdom, although there are many unavoidable obstacles ahead," KCNA said, making no mention of the breakdown of the high-stakes summit.

DPRK FM Ri Yong Ho disputes Trump's reason for summit collapse

The report came hours after DPRK Foreign Minister Ri Yong Ho held a highly unusual late-night press conference, denying Trump's claims that Pyongyang was seeking a complete lifting of sanctions.

Ri told reporters his country had offered to dismantle its Yongbyon nuclear plant in exchange for partial sanctions relief, while Trump had earlier said that Pyongyang had demanded the lifting of all sanctions imposed over the country's banned nuclear weapon and ballistic missile programs.

"What we proposed was not the removal of all sanctions, but they are partial removal," Ri said, adding the DPRK only asked for those sanctions impeding the livelihood of its people to be removed first.

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Ri said Pyongyang's position won't change even if U.S. seeks further talks.

Trump: Talks with Kim 'productive' but sanctions will continue

During a press conference after his second summit with Kim in Hanoi, Trump told reporters on Thursday that he had a "very productive" time with Kim, but he decided not to sign anything at this time.

He also said the DPRK wants all sanctions lifted but the U.S. is not willing to do so.

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A day after Trump's remarks, U.S. Secretary of State Mike Pompeo, while rejecting the claims made by his DPRK counterpart, said that the DPRK had sought full sanctions lifting but lacked complete clarity on what it was prepared to offer on dismantling the Yongbyon nuclear facility.

"They were pretty expansive with respect to what they are prepared to do at Yongbyon but there was still not complete clarity with respect to full scope of what it is they were prepared to offer," Pompeo told a news conference on Friday during a short stop in Manila.

He said that the U.S. is "anxious" to get back to negotiating table after the Hanoi summit failed to reach a deal.

"We are anxious to get back to the table so we can continue the conversation that will ultimately (bring) the peace and stability, better life for the North Korean people and (bring about) a denuclearized North Korea."

Pompeo said these "expansive" issues will be clarified in future meetings between the two sides. "It's one of the reasons I hope we can get back so we can put some definition around that," he said.

Chinese FM urges patience in DPRK-U.S. talks

During a meeting with DPRK Vice Foreign Minister Ri Kil Song on Thursday in Beijing, shortly after the end of the Trump-Kim summit, Chinese State Councilor and Foreign Minister Wang Yi urged the two sides to stay committed to the goal of achieving complete denuclearization of the Korean Peninsula and building a peace regime.

Wang called on Pyongyang and Washington to maintain patience, continue their dialogue, and meet each other halfway, adding that China is willing to continue playing a constructive role in issues related to the peninsula.

Commenting on the summit, Wang said DPRK-U.S. talks have entered a "deep-water zone" and it is inevitable that difficulties would emerge in one way or another. He underscored China's optimism in the prospect of the talks.

Russia hails readiness of U.S., DPRK to continue dialogue

Moscow on Thursday welcomed the intention of both Trump and Kim to continue bilateral dialogue on the Korean Peninsula's situation.

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In response to the result of the second Kim-Trump summit, Kremlin spokesperson Dmitry Peskov said Thursday, "From official statements, statements by President Trump himself and other high-ranking representatives of the White House, we understand that the negotiation process has not been interrupted, which is certainly positive."

"But, at the same time, it was probably not possible to reach any tangible agreements for the time being," he told reporters.

UN praises 'courageous diplomacy' at U.S.-DPRK summit

UN Secretary-General Antonio Guterres praised the U.S.-DPRK summit as "courageous diplomacy" on Thursday even though no agreement was reached, and expressed hope that talks will continue.

Guterres "appreciates the effort that was made in those discussions, regardless of the results, of the outcome that we saw," said Stephane Dujarric, the spokesperson for the UN.

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"Courageous diplomacy has established the foundation to advance sustainable peace and the complete and verifiable denuclearization of the Korean Peninsula.We all very much hope that these discussions will continue in that direction." 

The spokesperson stressed that world diplomats were clear-eyed about the prospects for a quick deal on dismantling DPRK's nuclear and ballistic missile programs.

ROK's Moon: Trump, Kim make 'meaningful progress' 

Republic of Korea (ROK) President Moon Jae-in Friday said the Hanoi summit between Kim and Trump had made a "meaningful progress", despite it breaking up without a nuclear deal.

"The two leaders had conversations at length, enhanced mutual understanding and built more trust," Moon said in a speech commemorating the 100th anniversary of the March First Movement against Japanese colonial rule. 

The ROK president said Kim and Trump moved closer to normalizing relations with the discussion of liaison offices in both countries. Calling the no-deal summit "a process going toward a higher-level agreement," Moon vowed to help Kim and Trump reach a "complete agreement."

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(With inputs from agencies)