The threat came as the South's army, navy, air force and marine corps launched an intensive military drill on and around Yeonpyeong Island in memory of the incident in which four people were killed in November 2010.
"Three years ago the baptism of retaliatory fire was limited to Yeonpyeong, but next time the presidential Blue House and all headquarters of the puppet regime will be targeted," the North's Korean People's Army said in a statement.
"If the South recklessly provokes us again, the sea of fire at Yeonpyeong will turn into a sea of fire at the Blue House," it said.
"Park Geun-Hye and her clique must find a painful lesson in the shameful defeat inflicted upon the South," it said, citing the South's president by her name without any title."
Three years ago on Saturday, North Korea bombarded the island of Yeonpyeong after warning the South against conducting a live gunfire drill in what the North claims as its territorial waters.
The attack killed two South Korean marines and two civilians in one of the most serious border incidents since the 1950-1953 Korean War.
Most islanders fled to the mainland after the attacks but have since returned home.
In the intervening three years, the island has built new fortifications, increased the number of troops three-fold and deployed new weapons including missiles, anti-battery radars and helicopters.
The maritime boundary - the scene of bloody clashes in 1999, 2002 and 2009 - is not recognised by Pyongyang, which argues it was unilaterally drawn by the US-led United Nations forces after the Korean war.
North Korea's military threatened to attack the island at the time of the shelling anniversary last year, saying its only regret was not sending Yeonpyeong "to the bottom of the sea" and adding it would not miss the opportunity if "warmongers" provoked it again.
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