The first meeting took place in 2000 between Kim Dae-jung, the then South Korean president, and Kim Jong-Il.
North Korea said urgent recovery work need to be carried out.
South Korea has offered an emergency aid package of more than $7m to the North after days of flooding brought havoc to large parts of the country, sparking fears that existing food shortages might worsen.
The North says the floods have left at least 80 people dead, many more missing, and about 300,000 others homeless.
In addition it says about 10 per cent of the country's farmland has been destroyed.
The US has also said it will give $100,000 to relief groups for emergency supplies, but international aid officials say they are still awaiting approval from North Korean authorities for food deliveries to begin.
According to aid groups, tens of thousands of houses and hundreds of bridges have been destroyed, water and power supplies shut down and railroads washed away.
Rising waters have also ruined crops and swamped more than 90,000 hectares of farmland in a country that already faced a serious food shortage.
The South Korean aid package includes packs of instant food, water, medicine, blankets and other supplies to be sent by sea and land.
South Korea is expected to discuss the details of transporting the aid with officials from the Red Cross and the North.
"The flood damage in the North is heartbreaking"
Lee Jae-joung, South Korea Unification Minister
Lee Jae-joung, South Korea's unification minister, said they wanted to provide immediate help on grounds of "humanitarianism and brotherly love".
"Considering the large-scale damage and the urgency of the people who have been displaced, we plan to provide the emergency aid as swiftly as possible," he said. "The flood damage in the North is heartbreaking."
He said Seoul has promised additional aid later, including equipment needed for recovery work.
An estimated 23 million people or 10 per cent of North Korea's population were killed in a famine in the second half of the 1990s, partly blamed on flood damage to farmland.
In New York, Margareta Wahlstrom, the UN assistant secretary-general and deputy emergency relief coordinator, said on Thursday heavy rains and flooding had "very badly affected" four southern provinces where North Korea's agricultural production is based.