SEOUL, South Korea — North Korea reopened a border hotline with South Korea on Wednesday, restoring a channel of direct dialogue and signaling a possible thaw in relations between the two Koreas after years of hair-trigger tensions.

The return of the telephone hotline at the village of Panmunjom, which straddles the Demilitarized Zone, the world’s most heavily guarded border, came two days after North Korea’s leader, Kim Jong-un, made a rare overture to the South.

In his New Year’s Day speech, Mr. Kim continued his nuclear threat against Washington, saying he had a “nuclear button” ready to launch a weapon against any target in the United States. But he also proposed negotiations with South Korea to discuss easing military tensions on the divided Korean Peninsula and his country’s possible participation in the Winter Olympics, which are being held in the South Korean town of Pyeongchang next month.

The fast-moving political developments have given new hope for a warming of ties between the two longstanding enemies.