US President Donald Trump (right) and DPRK leader Kim Jong-un take a walk after their first meeting at the Sofitel Legend Metropole Hanoi hotel in Hanoi, Vietnam, Feb 28, 2019. (EVAN VUCCI / AP)

WASHINGTON - US President Donald Trump said on Thursday it was possible for him to hold a third meeting with the top leader of the Democratic People's Republic of Korea (DPRK), Kim Jong-un.

When asked by reporters if he plans to meet Kim for a third summit, Trump said: "It could happen. A third summit could happen. And it's step by step." 

Trump, together with the Republic of Korea's President Moon Jae-in, made the remarks to the media before their bilateral meeting at the White House.

According to the full transcript provided by the White House, when asked by reporters if he plans to meet Kim for a third summit, Trump said: "It could happen. A third summit could happen. And it's step by step." 

READ MORE: Seoul: US, DPRK officials to meet in Asia ahead of summit

"It's not a fast process; I've never said it would be. It's step by step," he said. "I enjoy the summits. I enjoy being with the Chairman. I think it's been very productive."

When asked if a three-way summit with Kim and Moon is also possible, Trump said "that could happen also."

For his part, Moon said the personal diplomacy between Trump and Kim has brought "dramatic, significant reduction of military tension on the Korean Peninsula."

"Now peace has prevailed," he said. "Now we believe that you will be able to solve this problem through a dialogue."

Noting that "the Hanoi Summit is not actually -- was not a source of disappointment, but it is actually the part of a bigger process that will lead us to a bigger agreement," Moon said that efforts need to be made so as to "maintain the momentum of dialogue and also express the positive outlook, regarding the third US-DPRK summit, to the international community that this will be held in the near future."

After ending the summit in Vietnam's Hanoi on Feb 28 without an agreement, Trump told a press conference that Kim demanded relief from sanctions against Pyongyang "in their entirety" in exchange for denuclearizing a "large portion" of the DPRK's nuclear program, something the US could not agree to.

READ MORE: Trump: Deal with Kim thwarted by DPRK sanction demands

Dismissing Trump's claim, DPRK Foreign Minister Ri Yong-ho has said the DPRK only proposed partial removal of the sanctions, wanting those impeding the livelihood of their people to be removed first.

Wu Haitao, China's deputy permanent representative to the UN, said on Wednesday that for dialogue to continue and make headway, the key is to address the legitimate concerns of the parties concerned in a balanced manner, and advance denuclearization and the establishment of a peace mechanism for the peninsula by following a phased approach with synchronized steps as a package solution.