Seoul, South Korea (CNN) -- South Korean Defense Minister Kim Tae-young resigned Thursday, according to the South Korean presidency.
"The president has just accepted the defense minister's resignation," according to a spokesman for the Presidential Blue House.
Kim, a former general, came under heavy criticism after the March sinking of the South Korean vessel Cheonan and again after the North Korean shelling of the South's Yeonpyeong Island on Tuesday.
North Korea has been blamed by the South and other nations for the Cheonan incident, in which 46 soldiers were killed, but has denied responsibility. It has blamed South Korea and the United States for the Yeonpyeong incident, in which two South Korean marines and two civilians were killed and 15 others injured.
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South Korean lawmakers from both parties alleged that South Korean forces were unprepared for the North Korean attacks. Lawmakers demanded Kim's resignation earlier Thursday.
President Lee Myung-bak also drew criticism for his first statements after the Yeonpyeong attack, in which he urged de-escalatory measures.
Earlier Thursday, North Korean state media said the nation will launch additional attacks on South Korea if the South continues "reckless military provocation."
Pyongyang "will deal without hesitation the second and third strong physical retaliatory blow" if provoked, its KCNA news agency said.
As an example of provocation, it indirectly referred to a military drill that South Korea and the United States plan to hold in the Yellow Sea starting Sunday.
Meanwhile, South Korea said Thursday that it will strengthen and supplement its rules of engagement in the Yellow Sea, following the incident on Yeonpyeong Island.
South Korea was holding annual military exercises near North Korea when Pyongyang started shelling Tuesday. Shells from the South's exercises landed in North Korean waters, KCNA said.
KCNA on Thursday continued its verbal offensive against the South Korean-U.S. military drill that is to start Sunday.
"The U.S. and the South Korean puppet forces are foolishly contemplating an additional provocation aimed to orchestrate another farce and charade such as the "Cheonan" case while kicking up rows and holding confabs one after another such as the declaration of a "state of emergency" and "a meeting of ministers in charge of security," far from drawing due lesson from the recent shelling," KCNA said.
The aircraft carrier USS George Washington on Wednesday sailed toward the Yellow Sea for the drill, which was billed as defensive.
"It is a long-planned exercise," said Adm. Mike Mullen, chairman of the U.S. Joint Chiefs of Staff.
"That said, it is meant to send a very strong signal of deterrence and also work with our very close allies in South Korea," Mullen said on CNN's "Fareed Zakaria GPS."
"We're very focused on restraint --- not letting this thing get out of control. The South Koreans so far have responded that way. Nobody wants this thing to turn into a conflict."
On Thursday morning, Lee and his economic and security ministers met in Seoul.
The meeting began with a moment of silence for the Yeonpyeong victims. After the meeting, South Korea said it would boost its rules of engagement in the Yellow Sea.
South Korean marine forces based in five islands near North Korea and the disputed Northern Limit Line also will be reinforced, a government spokesman said.
The tense maritime border between the two Koreas has become the major military flash point on the Korean peninsula in recent years.
The Yeonpyeong attack also will lead to a plan for civilian safety on the five islands in the Yellow Sea, the government spokesman said. No details were immediately offered about the plan, but Lee on Wednesday ordered the strengthening of civilian shelters on the islands.
The islands include Yeonpyeong and Baengnyeong, off which the South Korean warship Cheonan was sunk in March, killing 46 sailors. Seoul blamed Pyongyang for the torpedo attack, which the North has denied.
The Lee administration also will continue to closely monitor capital markets and foreign exchange rates, prepared to take preventative measures as needed, the spokesman said. The Yeonpyeong shelling sent ripples through South Korea's stock market, which has rebounded.
South Korea's economic and security ministries will cooperate closely, and the administration will publicize developments in real time to address major concerns and squelch rumors, the spokesman said.
The Yeonpyeong attack was the first direct artillery assault on South Korea since the Korean War ended in 1953.