"The U.S. should know that the button for nuclear weapons is on my table", he said, according to the Associated Press translation, in a speech carried by state television.
This week's exchanges follow a year dominated by fiery threats form Kim and U.S. President Donald Trump who vowed to destroy North Korea if threatened, even as U.S. diplomats pushed for a diplomatic solution.
North Korea would focus in 2018 on "mass-producing nuclear warheads and ballistic missiles for operational deployment".
Lee Hee-Beom, the head of the Pyeongchang Organising Committee for the Olympic Games (POCOG) told AFP: "We actively welcome the North's suggestion that it is willing to engage in talks for the participation in the Olympics".
Cho told a media conference he expects the two Koreas to focus on bringing a North Korean delegation to the Pyeongchang Winter Olympics, which begin next month, should the talks be held on January 9.
The South's state-run Institute for National Security Strategy, however, cautioned that a North Korean team is likely to come with strings attached, as the regime would see the move as a service that "helps" the South.
In the speech, Kim also stressed North Korea's economic achievements and noted the importance of improving the nation's standard of living, the AP reported.
Muslim women have applied to perform Haj without 'mehram', says Modi
I was amazed by spirit they had, the enthusiasm in their hearts and the dreams they nurtured". "Indian Democracy welcomes these new voters", he said.
South Korean President Moon Jae-in said on Tuesday the improvement of inter-Korean relations was linked to resolving North Korea's nuclear program, a day after the North offered talks with Seoul but was steadfast on its nuclear ambitions. This is the role that Seoul can play in making progress in inter-Korean relations, easing tensions on the Korean Peninsula and laying the foundation for denuclearization talks between the United States and North Korea.
Kim said in his televised New Year's address that the two Koreas should have "immediate talks" on the matter, Yonhap reported.
John Delury, a professor of worldwide relations at Yonsei University in Seoul, said Kim's message to Seoul was "more promising" than he had anticipated, addressing in a specific and actionable way South Korea's desire to make the Games a success.
North and South Korea have been divided by a demilitarised zone since the end of the 1950-53 Korean war.
"We've been preparing for the Olympics on the assumption that the North will eventually take part in the games", he said, adding that POCOG have in place protocols for accommodation and transport for the North's athletes.
North Korea conducted its sixth and most powerful nuclear test in September in defiance of global warnings and sanctions, raising fears of a new conflict on the Korean peninsula.
"I regret the government had even lost the flexibility to spend one day or two taking a deep breath and meticulously analysing Kim Jong Un's ulterior motive before hastily issuing a welcoming statement", he said.