South Korea on Tuesday renewed its call for North Korea to accept its latest dialogue offer, vowing to continue "multifaceted" efforts to resolve issues of war-torn families and ease border tensions.

The call came as North Korea fired a second intercontinental ballistic missile in less than a month Friday, spurning Seoul's proposals for talks.

Tuesday is the day on which the government offered to hold Red Cross talks to resume reunions for families separated by the 1950-53 Korean War.

"The government is calling on North Korea to respond to Seoul's dialogue offer. We will make multifaceted efforts to resolve humanitarian issues and ease military tensions," said a government official, without elaborating.

The issue of separated families is one of the most pressing humanitarian matters for the two Koreas as more aging Koreans have passed away without being able to meet with their kin on the opposite side of the tense border.

The South also previously offered to open military talks with the North on easing border tensions on July 21, but Pyongyang did not respond to it.