Reunions last happened in September and October 2009, and their potential renewal could signal an easing of tensions after the deadly sinking of a South Korean warship in March.
The North proposed that the two Koreas' Red Cross societies meet soon to discuss the gatherings. It proposed the reunions take place at the North's scenic Diamond Mountain on the Chuseok autumn harvest holiday, the North's official Korean Central News Agency reported.
Chuseok, which falls on Sept. 22 this year, is a major holiday for both Koreas, equivalent to Thanksgiving in the United States.
North Korea's Red Cross chief Jang Jae On expressed hope that "humanitarian cooperation between the North and the South would get brisk with the reunion of separated families and their relatives." Jang made the comment in a message sent to his South Korean counterpart on Friday, according to KCNA.
South Korea's Red Cross would consider the North's proposal and consult with the government, according to Kim Seong-keun, a South Korean Red Cross official in charge of inter-Korean cooperation.
The two sides last held Red Cross-brokered reunions for six days around Chuseok holiday in late September and early October last year. So far, more than 20,800 separated families have been reunited through brief face-to-face meetings or by video following a landmark inter-Korean summit in 2000.
Millions of families were separated by the division of the Korean peninsula in 1945 and the 1950-53 Korean War, which ended with a cease-fire, not a peace treaty, leaving the two countries technically at war. There are no mail, telephone or e-mail exchanges between ordinary citizens across the Korean border.
The North's offer is the latest in a series of conciliatory gestures by North Korea toward Seoul and Washington.
Last month, North Korea freed an imprisoned American during former President Jimmy Carter's rare trip to Pyongyang. Earlier this week, the North also released a seven-man crew of a South Korean fishing boat seized a month ago in its waters.
The North's overture also came days after flood-stricken North Korea requested a shipment of rice, cement and heavy equipment from South Korea to recover from recent flooding.
Seoul had offered to send aid worth 10 billion won ($8.5 million) despite tensions over the warship sinking that has been blamed on Pyongyang. The North has denied its involvement in the sinking that killed 46 South Korean sailors.
Meanwhile, there is widespread speculation that North leader Kim Jong Il may be preparing to give his youngest son, Kim Jong Un, a key Workers' Party position at the upcoming party conference as part of plans to extend the Kim dynasty into a third generation.