Seoul had proposed to hold rare inter-Korea talks this week at the border truce village of Panmunjom to ease hostilities after a series of missile tests this year.
"It is an urgent task to reduce tension between two Koreas... to achieve peace and stability of the Korean peninsula," defense ministry spokesman Moon Sang-Kyun said.
"We urge the North again to respond to our talks proposal," he said.
The military talks, if realised, would have marked the first official inter-Korea talks since December 2015.
The North has also remained silent on another offer made by the South's Red Cross to meet on August 1 and discuss potential reunions for families separated by the 1950-53 Korean War.
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Millions of families were separated by the conflict that sealed the division of the peninsula. Many died without getting a chance to see or hear from their relatives on the other side of the border, across which all civilian contacts are banned.
Monday's twin proposals are the first concrete steps towards rapprochement with the North since South Korea elected dovish President Moon Jae-In in May.
Moon has advocated dialogue with the nuclear-armed North to bring it to negotiating table and vowed to play a bigger active role in global efforts to tame the unpredictable regime.
His conservative predecessor Park Geun-Hye had refused to engage in substantive dialogue with Pyongyang unless it made a firm commitment to denuclearisation.
But Pyongyang has staged a series of missile launches in violation of UN resolutions in recent months -- including its first ICBM test on July 4 that triggered global alarm and a push by US President Donald Trump to impose harsher UN sanctions.
