As Pyongyang waits for the U.S. to change its stance, it will "keep increasing the defense capabilities", the North Korean leader stressed.
"It is essential for the USA to quit its current method and approach us with a new one", Kim said in a speech to the Supreme People's Assembly on Friday.
According to Kim, the problem lied in the "American-style way of dialogue" which amounted to making "unilateral" demands without being ready to "sit face-to-face with us and settle the problem".
"It seems like a positive message from the standpoint of possibly resuming the talks", said Dong-Yub Kim, a North Korea specialist at Seoul's Institute for Far Eastern Studies.
Kim has signed vague statements calling for the "complete denuclearisation" of the peninsula in his meetings with Trump and Moon.
Moon's visit was seen as an effort to revive nuclear disarmament talks between Washington and Pyongyang following the collapse of Trump's second summit with North Korean leader Kim Jong-un in February.
He also set the USA a deadline of "until the end of this year" to demonstrate that new talks could be more productive.
Trump became the first sitting USA president to meet a leader of North Korea after meeting Kim in June in Singapore.
Leader Kim Jong Un has made economic development the centerpiece of his strategy and told officials this week that building a self-supporting economy would be a blow to the "hostile forces" that have imposed sanctions on North Korea.
North Korean media touted Kim's "re-election" as chair of the State Affairs Commission as an expression of "the general will of all the Korean people" and their gratitude for Kim's "outstanding ideological and theoretical wisdom and experienced and seasoned leadership and demonstrating the politico-ideological might and tremendous power of socialist Korea on the highest level".
A senior administration official said Thursday that the US and the worldwide community had "clearly defined the scope" of North Korea's weapons of mass destruction and ballistic missile programs, have a shared understanding of what final, fully verified denuclearization entails and what meaningful progress toward that goal looks like.
Speaking alongside South Korean President Moon Jae-in, Trump on Thursday expressed openness to "smaller deals" with the North.
"The confrontation is likely to continue as there's a low chance that the U.S. will change its position", Mr Shin said.
In Hanoi, Pyongyang offered to close its main nuclear facility in return for sanctions relief, but Washington sought a "big deal" comprising - in details which have emerged post-summit - the demand that North Korea surrender all its nuclear arms and weapons of mass destruction. DPRK stands for the North's official name, Democratic People's Republic of Korea.
Kim Yong-chol was considered a controversial choice for point man because he is held responsible for North Korea's attack on the South Korean warship Cheonan in 2010. In the months leading up to the talks, Pyongyang froze its nuclear and ballistic missile tests and demolished the only known nuclear test site.
"I make it clear once again that it is my unwavering determination to turn the North-South ties into those of durable and lasting reconciliation and cooperation by holding hands with the south Korean authorities and to write a new history of the nation, peaceful and co-prosperous", he said.