The family members will be sent to Seoul to see the alleged defectors, via the truce village of Panmunjom, Xinhua news agency cited North Korean official KCNA news agency as reporting.
North Korea made the decision after the families requested to meet face-to-face with their daughters, who they said had been abducted by South Korean intelligence to Seoul, reported the KCNA.
It carried a statement issued by the chief of the central committee of North Korea's Red Cross Society.
The statement said the "group defection" as claimed by the South Korean government was, in fact, kidnapping by deception and conciliatory measures, and urged the country's Red Cross Society to facilitate the meeting in light of humanitarian principles.
On April 8, Seoul's Unification Ministry said a group of 13 people from North kOrea working in an overseas restaurant defected to South Korea.
South Korean media said this marked the first time that a group of North Korean citizens working at the same overseas restaurant defected to South Korea.
South Korean media reported that the 13 people -- 12 waitresses and one manager -- chose to defect to the south because they were pressured to turn in their revenues back to North Korea.
Seoul also advised South Korean nationals not to visit overseas restaurants run by North Koreans to cut North Korea's source of foreign currency.
A spokesman for North Korea Red Cross Society last week called this "a group abduction" and "a hideous crime" against North's dignity and its social system, and demanded the South Korean government return the 13 North korean nationals immediately.
On Monday, seven waitresses who worked at the same restaurant and later returned to North Korea told the CNN in an interview how the restaurant manager tricked them and worked together with South Korean authorities to lure their colleagues to Seoul.