SEOUL—South Korea sought unsuccessfully to raise the North’s nuclear program during bilateral talks, but the two sides reached a deal for Pyongyang to participate in the Winter Olympics and agreed to revive cross-border military communications, as Seoul pursues a diplomatic path to try to end the long-running standoff.

Tuesday’s face-to-face discussions at the demilitarized zone that divides the peninsula were the two Koreas’ first since December 2015, and they came as the Trump administration leads a global push to isolate the North, which has been hit with tougher international sanctions in response to its weapons tests.

A joint statement released after the talks contained no mention of the North’s atomic-weapons program, and South Korean officials said Pyongyang’s delegates had voiced anger when Seoul broached the North’s weapons program.

In a briefing after the talks, North Korea’s chief delegate, Ri Son Gwon, said it was ridiculous to raise the subject of the North’s nuclear weapons, which he said were “strictly aimed at the U.S.”

“They do not target our brethren, nor do they target China and Russia,” he said.