Mr Kim did not explicitly mention a summit with the United States president at the Workers Party meeting on Monday.
But the North remained publicly silent for weeks after its leader's invitation to talks was first delivered to Trump by South Korean officials.
"They've said so. We've said so", Trump continued.
They appear, however, to be much more low-key this year.
For decades, North Korea has dangled the prospect of "denuclearization" - freezing its nuclear weapons programs - but only if the USA withdraws its forces from South Korea.More news: Who is Sathish Sivalingam?
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The meeting will be the third summit between the two Koreas.
Xi Jinping was also pleased that Kim Jong-un declared the need for South Korea and the United States to "create an atmosphere of peace and stability" and to take "phased, synchronized measures to achieve peace".
The US later heard from other countries, including China, where Kim paid a rare visit, that the North was serious about the offer. Trump said: "They've said so".
Trump's upcoming summit with North Korean leader Kim Jong-un will be an historic encounter between two supremely self-confident, headstrong, and mercurial men, each seeking the other's surrender.
Bolton, in a March interview, said that his preference will be for precisely a Libya-style settlement of North Korea's nuclear program, which remains both unrealistic and dead on arrival.
The North has previously demanded the withdrawal of USA troops based in the South and the end of the security alliance between Seoul and Washington - an extraordinary concession that it is hard to imagine any previous USA president acceding to.
The official accompanied the North's Foreign Minister Ri Yong-ho at a ministerial-level meeting of the Non-Aligned Movement (NAM) in Baku, Azerbaijan, last week.