The offer came a day after the two Koreas agreed to hold their first official dialogue in more than two years to discuss the North's participation in next month's Winter Olympics in South Korea.
The tentative rapprochement comes after the North's leader Kim Jong-Un warned in his New Year speech that he had a nuclear button on his desk, but also said Pyongyang could send a team to the Pyeongchang Winter Olympics.
Seoul responded with an offer of talks and earlier this week the hotline between the neighbours was restored after being suspended for almost two years.
The ministry said on Saturday that the South had suggested Unification Minister Cho Myung-Gyon lead the delegation to the meeting in the truce village of Panmunjom on Tuesday.
He would be accompanied by four other officials, including two vice ministers -- one of whom is in charge of sports -- the South said as the two Koreas discussed the size and formation of delegations by fax.
"We've been informed from the North's side that there won't be any response today," a unification ministry official was quoted as saying by Yonhap news agency.
Kim said in his New Year speech that his country wished success for the Olympics, to be held from February 9-25.
On Saturday, North Korea's Olympic representative said the hermit state was "likely to participate" in the games, Kyodo news agency reported.
The two Koreas have been separated by the world's most heavily militarised border since the Korean War ended in a stalemate in 1953.
In recent months, the North has held multiple missile launches and its sixth and most powerful nuclear test -- purportedly of a hydrogen bomb -- in violation of UN resolutions banning such activity by the isolated nation.
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