The planned exercise will take place close to Yeonpyeong Island, which North Korea shelled yesterday.
In November, North Korea shelled Yeonpyeong Island, killing two South Korean marines and two civilians.
Late in 2010, North Korean artillery units fired shells onto and around Yeonpyeong Island in disputed waters.
The Uriminzokkiri website, linked to the regime, mentioned targets including Yeonpyeong island, which was attacked by Northern forces in 2010.
In 2010, it shelled South Korea's Yeonpyeong island, causing four deaths.
Incidents like Yeonpyeong Island shelling are likely to scare markets, which damages the economy, and voters are likely to eventually blame the government for this damage.
Late last week he gave similar instructions to troops near Yeonpyeong Island, the scene of shelling in November 2010 that left four South Koreans dead, KCNA said.
The idea that strong words could act as a deterrent to North Korean actions has gained traction since the lethal shelling of South Korea's Yeonpyeong Island in 2010.
But North Korean state media have in recent days reported several visits by leader Kim Jong-un to military units near the disputed western maritime border, including near Yeonpyeong island.
The South Korean military said Thursday that its drills will take place in the seas southwest of Yeonpyeong Island between December 18 and 21, but bad weather forced a delay Saturday.
After the sinking of the corvette Cheonan and shelling of Yeonpyeong Island in 2010, the South has had enough of the North's misbehavior and a plan for retaliation is ready in case of another attack.
Meanwhile, the International Criminal Court said it would investigate suspected war crimes by the North after the shelling of Yeonpyeong island on 23 November, in which two South Korean marines and two civilians were killed.
Kim Kyok Sik, another family friend and leader of forces on the inter-Korean border, is believed by analysts to have directed the 2010 attacks on the South Korean warship Cheonan and Yeonpyeong Island, which is controlled by South Korea.
But our main focus is in our alignment with our allies in South Korea, continuing to deter provocation such as we encountered last year in 2010 with the sinking of the corvette Cheonan, and the attack against Yeonpyeong Island.
WHITEHOUSE: Press Briefing with Ben Rhodes and Admiral Robert Willard
Without its dangerous arsenal, it's unlikely Pyongyang would have gotten away with the 2010 shelling of Yeonpyeong island, when it killed two South Korean marines and three civilians, sent the population fleeing in panic and set homes and forests on fire.
The drills were planned well before North Korea shelled the South Korean island of Yeonpyeong last month, killing two marines and two civilians.
Japan's government has been on high alert since North Korea shelled the island of Yeonpyeong on 23 November, killing at least four South Koreans.
It has stayed open during even the tensest times between the two countries, including the North's surprise shelling last year of the inhabited South Korean island of Yeonpyeong.
On Sunday North Korea's new leader Kim Jong-un visited front-line military units, including one said to be responsible for an attack on the South Korean island of Yeonpyeong in 2010.
BBC: North Korea warning as US and S Korea begin joint drill
Last year's presumed attack on the South Korean naval vessel, the Cheonan, in March, killing 46 sailors and the artillery barrage on civilians living on the island of Yeonpyeong in November were only the latest in a string of lawless acts of aggression.
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