The effort is among the steps promised by North Korean leader Kim Jong Un and South Korean President Moon Jae-in to improve relations that had deteriorated over the North's nuclear and missile programmes.
Friday's meeting, which began at 0100 GMT in a hotel in North Korea's tourist destination of Mount Kumgang, comes after the two sides agreed in April to pursue a reunion to mark a common national holiday in August.
"We should make active efforts for good results today by trusting and being considerate of each other," said Pak Yong Il, the leader of the North's delegation.
"We should also part with the past and go down the road our leaders have forged for us," added Pak, the deputy head of the North's agency to promote reunification, the Committee for the Peaceful Reunification of the Fatherland.
South Korean officials have called for the visits between separated families to resume as a "humanitarian and human rights issue", especially since many individuals are now in their 80s.
Past reunions, some televised, have often unleashed floods of tears, with face-to-face encounters ending in painful separations. The last reunions were held in 2015.
The South has also sought to resume video conferences and the delivery of letters among families divided by the border.
Since 2000, about 23,676 separated Koreans, from both North and South, have met or interacted through videolink as part of the programme, the Hyundai Research Institute thinktank said.
By March, 56 percent of the South's 131,531 applicants for such reunions had died, it added.
Several of the women said in May they were coerced into leaving, while South Korean officials said they were trying to verify their accounts.
As recently as May the North Korean Red Cross organization urged South Korea to return the women "without delay".
South Korean representatives to the Red Cross talks left on Thursday for the South's eastern border town of Goseong and set out for the meeting venue in North Korea early on Friday.
"We'll have good discussions on humanitarian issues with North Korea and how we'll assuage the pain of the 57,000 family members separated," Park Kyung-seo, the Korean Red Cross president in Seoul who heads the South's delegation, said on Thursday.
Ties have warmed as relations between North Korea and the United States have improved after Kim met U.S. President Donald Trump in Singapore last week in the two nations' first summit.
The 1950-53 Korean War was concluded only with a truce, not a peace treaty, leaving the combatants technically still at war.
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