GOYANG, South Korea—The leaders of North and South Korea agreed to work toward a peace agreement to formally end the Korean War 68 years after it began, but Friday’s historic talks avoided specifics about Pyongyang’s nuclear weapons ahead of its planned summit with President Donald Trump.

After an 8½-hour meeting in the demilitarized zone that was heavy on shows of amity between Kim Jong Un and Moon Jae-in, his South Korean counterpart, both men agreed to dial down tensions and start talks with the U.S.

Fighting...