SEOUL, South Korea — On both sides of the divided Korean Peninsula, the timing seems right.

The New Year’s Day proposal by North Korea’s leader, Kim Jong-un, for direct talks with South Korea came as sanctions appear to be biting, with reports of shortages in the North and new pressure by Washington to intercept ships engaged in fuel smuggling.

The initiative was quickly embraced by South Korea’s president, Moon Jae-in, who sees his first concrete chance to carry out his campaign agenda of engaging with the North, while also easing tensions as Mr. Trump’s warlike threats have rattled his country.

In a telephone message delivered through the restored cross-border hotline on Friday, North Korea accepted the South’s proposal that the two sides begin talks on Tuesday, South Korean officials said. The talks, to be held in the border village Panmunjom, will be the first high-level inter-Korean dialogue in two years.

But if this is a potential opening for a thaw, it is a small one. Skepticism abounds not only in Washington but also among South Koreans.