SEOUL, South Korea — Beyond a New Year’s declaration by North Korea’s leader, Kim Jong-un, that he would move to the mass production of nuclear weapons and intercontinental missiles in 2018 lies a canny new strategy to initiate direct talks with South Korea in the hope of driving a wedge into its seven-decade alliance with the United States.

Mr. Kim, perhaps sensing the simmering tension between President Trump and President Moon Jae-in of South Korea, called for an urgent dialogue between the two Koreas before the opening of the Winter Olympics in the South next month.

The strained relationship between the allies has been playing out for months, as Mr. Moon, a liberal, argued for economic and diplomatic openings with the North, even as Mr. Trump has worked hard to squeeze the North with increasingly punishing sanctions. Mr. Moon also angered Mr. Trump and his aides in recent months by suggesting he holds what he called a veto over any American pre-emptive military action against the North’s nuclear program.

Until now Mr. Kim has largely ignored Mr. Moon, whom the North Korean media has portrayed as a spineless lackey of the United States. But the dramatic shift in tone and policy, toward bilateral talks between the two Koreas, suggests that Mr. Kim sees an opportunity to develop and accentuate the split between Mr. Moon and Mr. Trump, betting that the United States will be unable to mount greater pressure on the North if it does not have South Korean acquiescence.