Park's orders followed the North's surprise offer today for an end to "all acts of provoking and slandering" from January 30 and its call for steps to ease tensions around the disputed Yellow Sea border, the scene of naval clashes in the past.
The North also renewed calls for South Korea to scrap its planned joint military drills with the United States, an exercise which Pyongyang routinely condemns as provocative rehearsals for invasion.
"Park ordered the defence minister and other security-related ministers to make more efforts to keep an airtight security posture against provocations at a time North Korea is conducting a flurry of propaganda offensives," Yonhap quoted Lee as saying in New Delhi where Park is currently on a state visit.
Analysts have said both sides were jockeying for the moral high ground ahead of what is gearing up to be a re-run of last year's display of military brinkmanship, which triggered global concerns of a full-scale conflict.
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Last year's exercises were held following North Korea's third and largest nuclear test which prompted months of escalated military tensions that saw Pyongyang issue apocalyptic threats of nuclear war against Seoul and Washington.
North-South Korean ties are currently in a state of watchful limbo, with both sides voicing willingness to improve relations while accusing the other of lacking sincerity.
Earlier this month, Park had called for the resumption of reunions for families separated by the Korean War. But the North rejected the proposal, citing the South-US exercises as a major barrier.