Warning her against “slandering”, North Korea told Park Geun-hye to behave with discretion to avoid “horrible disaster”.
Park Geun-hye’s comments came as she marked three years since the deadly sinking of a South Korean warship.
Overnight, meanwhile, South Korea briefly placed a border military unit on its highest alert.
The alert happened early on Wednesday after a South Korean soldier discovered a “strange object” at the border, military officials said. The alert prepares troops for a possible incursion from North Korea.
The soldier, who was at a military post in Hwacheon, in South Korea’s north-eastern Gangwon province, threw a grenade at the object at around 02:30 local time, officials said. The alert was lifted at 09:20 local time.
Tensions are high on the Korean peninsula following multiple threats from North Korea in recent days.
The border incident came hours after North Korea said it had ordered artillery and rocket units into “combat posture” to prepare to target US bases in Hawaii, Guam and the US mainland.
Pentagon spokesman George Little said that North Korea’s threats “followed a pattern designed to raise tensions” and that North Korea would “achieve nothing by these threats”.
North Korea has been angered by fresh UN sanctions imposed after its nuclear test on February 12. It also bitterly opposes joint US-South Korea military drills that are currently taking place.
In its latest statement, carried by state-run KCNA news agency, North Korea told President Park Geun-hye that its patience was being pushed to the limit.
“She should behave with discretion, clearly mindful that a wrong word may entail horrible disaster at a time when the North-South relations are being pushed to the lowest ebb and the danger of an all-out war is increasing on the Korean Peninsula,” it said.
“If she keeps to the road of confrontation like traitor [former president] Lee [Myung-bak], defying the warnings of the DPRK [North Korea], she will meet a miserable ruin.”
On Tuesday Park Geun-hye had told the North its only path to survival lay “in stopping provocations and threats, abandoning its nuclear weaponry and missiles”.
Park Geun-hye spoke in Daejeon, where the 46 sailors who died when the Cheonan warship sank on 26 March 2010 are buried. South Korea says a North Korean torpedo sank the ship; Pyongyang denies any role in the incident.
The South Korean president has spoken in the past of a desire for more dialogue with North Korea but current tensions are obstructing movements to improve ties.
Late on Tuesday, North Korean state-run media also reported that its top political bureau would soon hold a rare meeting to discuss “an important issue for victoriously advancing the Korean revolution”.
It did not specify the issue, or the date of the meeting.
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