SEOUL, South Korea — South and North Korea held a high-level meeting on their border on Saturday and agreed to meet again on Sunday, South Korean officials said, apparently easing, at least temporarily, a tense standoff that has prevailed since the countries exchanged artillery fire two days ago.

The meeting, which began in the border village of Panmunjom on Saturday evening, continued until early Sunday morning, said Min Kyung-wook, spokesman for President Park Geun-hye of South Korea. Mr. Min said it included top policy makers from both sides: Kim Kwan-jin, Ms. Park’s senior national security adviser, and Vice Marshal Hwang Pyong-so, North Korea’s most powerful military officer after Kim Jong-un, the supreme leader, who holds the rank of marshal.

“Both sides had comprehensive discussions on how to resolve the current situation and how to improve South-North relations in general,” Mr. Min said. The negotiators agreed to meet again on Sunday afternoon to try to narrow their differences, he said.

North Korea’s state-run news media, reporting on the talks, did something it had not done for several years, raising hopes for the border meeting: It referred to South Korea by its official name, the Republic of Korea, instead of using the North’s standard derogatory reference to “South Korean puppets.”