SEOUL—The leaders of Japan and South Korea pushed for a quick resolution to a long-standing dispute over the tens of thousands of Korean and other women in World War II who were made to serve as prostitutes for Japanese troops.

“The two countries agreed to accelerate the talks [over so-called comfort women] and aim to reach an agreement as early as possible,” Japan’s Prime Minister Shinzo Abe said Monday after his 100-minute conversation with South Korean President Park Geun-hye at her Blue House presidential office, in their...