North Korea's Deputy Foreign Minister Choe Son Hui said last month that Kim would soon make clear his post-Hanoi position.
But if an initial meeting between Trump and Kim in Singapore a year ago broke the ice, the follow up in Hanoi ended with no progress on U.S. demands for North Korea to start dismantling its nuclear weapons programme or North Korea's desire to see an easing of worldwide sanctions.
Moon has arrived in Washington DC on Wednesday in order to discuss the second summit between the United States and North Korea in Vietnam, which was ended abruptly without reaching any nuclear agreement.
The 687 lawmakers in the nominal parliament are elected for a period of five years, while turnout at the polls in March was over 90 per cent.
Choe was one of the most powerful officials in North Korea as head of the Workers' Party of Korea Organization and Guidance Department (OGD), according to database North Korea Leadership Watch.
Kim Yong Nam, the now-91-year-old who held the position of the North's head of state - an nearly entirely ceremonial role - for nearly 20 years, was replaced by Choe Ryong Hae, the state-run KCNA said.
It was the South Korean President's first meeting with Trump since Trump's unsuccessful summit with Kim in Vietnam in February.
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 that "it could happen".
Jon, who spoke through Mr. Kim Chin Il, First Secretary of the Embassy, an interpreter, said although DPRK had established relationship with Nigeria, much could be done to deepen it.
Trump and Moon's remarks come after Kim on Wednesday vowed never to give in to sanctions, adding that Pyongyang needs to deliver a "serious blow" to those imposing it.
During a meeting with Moon, Trump said his government wants sanctions on North Korea to stay in place though he didn't rule out a third summit with Kim.
'I think it likely that there will be some sanctions relief, especially as Trump has indicated some flexibility, albeit limited, ' Columbia University Professor and Korea Society director Stephen Noerpe told Asia Times.
The summit in Hanoi fell apart as North Korean leader Kim and U.S. President Donald Trump failed to find common ground over how to match Pyongyang's denuclearization steps with Washington's sanctions relief.
Shortly after the Hanoi summit, a series of satellite images emerged suggesting increased activity at the North's Sohae rocket site, triggering an worldwide alarm that the nuclear-armed state might be preparing a long-range or space launch. But the younger Kim has more openly embraced many of those market changes, and North Korea has sought to ease sanctions and attract more private investment.
When the right time comes, "a lot of countries will be helping", he said.