Mr. Kim ordered all front-line units to go on a "semi-war state," one of his country's highest military alerts, from 5 p.m. Friday during an emergency meeting of his Central Military Commission, the north's official Korean Central News Agency said on Friday.
North Korea issued the same sort of alert in 1968, when it hijacked the American spy ship Pueblo, and in 1993, when the standoff with Washington over its nuclear weapons program first flared.
"Commanders were appointed and dispatched to the relevant sectors of the front to command military actions" to destroy the South Korean loudspeakers and counter possible retaliations from the South, the North's news agency said. The front-line units "should enter a wartime state to be fully battle ready to launch surprise operations," it added.
The Kim regime has frequently issued bellicose statements, claiming that the divided Korean Peninsula was "on the brink of war" whenever the United States and South Korea conduct one of their joint annual war games, which it called rehearsals for invasion. But the latest threat followed a highly unusual exchange of artillery shells across the two Koreas' land border.
South Korean military radar detected what appeared to be a North Korean rocket landing in Yeoncheon County, near the border north of Seoul, at 3:52 p.m. Thursday, the Defense Ministry said in a brief statement.
Twenty minutes later, the North carried out another attack, said Col. Jeon Ha-gyu, a South Korean military spokesman. The South Korean news agency Yonhap quoted unnamed military sources as saying that the second attack involved several rounds from a 76.2-millimeter direct-fire weapon.
South Korea responded by firing "dozens" of shells from a 155-millimeter artillery unit, targeting the rocket's launching point in the North, the ministry said.
"Our military raised its vigilance to the highest level and is closely watching the movement of the North Korean military, ready to respond strongly and decisively to any further provocations from the North," Colonel Jeon said.
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About 220 people from two villages in Yeoncheon were evacuated into underground shelters, said Hong Seong-beom, a county official. Mr. Hong said there were no immediate reports of damage.
North Korea said the South fired 36 artillery shells across the border, some of them falling near its guard posts but not causing injuries, the headquarters of the North's military, known as the People's Army, said in a statement carried by the Korean Central News Agency.
North Korea denied the first rocket attack but did not comment on what South Korea said was a second attack. "This reckless provocative mania should never go unpunished," the North said, reporting the emergency meeting of its Central Military Commission.
The North's attacks followed repeated threats to attack the loudspeakers that South Korea had turned on along the border last week to broadcast propaganda.
President Park Geun-hye convened an emergency meeting of the South's National Security Council on Thursday and ordered the military to "deal resolutely with any North Korean provocations," said her spokesman, Min Kyung-wook.
The exchange of fire was the first serious armed clash between the countries since North Korea carried out an artillery attack on a South Korean border island in 2010, killing two marines and two civilians. At the time, South Korea retaliated by pounding gun positions in the North.
In recent years, the two sides have exchanged minor fire, mostly harmless warning shots, across their border. In May of last year, a North Korean patrol boat fired two rounds of artillery, which fell 490 feet from a South Korean Navy ship in waters near a disputed western sea border. The South's ship responded by firing several rounds of its own.
Tensions have been on the rise along the countries' heavily armed 155-mile border since Aug. 4, when two South Korean border guards were seriously wounded by land mines that the South said were planted by the North. North Korea has denied planting the mines.
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In retaliation, South Korea last week began using loudspeakers along the border to broadcast propaganda messages into North Korea, a tactic dating from the Cold War that had not been used in 11 years. The North turned on propaganda loudspeakers of its own, and it threatened to attack South Korea's.
"The fact that the North only launched one rocket without hitting any South Korean loudspeaker indicates that the North meant it as a warning," said Koh Yu-hwan, a North Korea expert at Dongguk University in Seoul.
Mr. Koh said that the North was unlikely to escalate the exchange of fire into a major skirmish, given the large-scale joint military exercise — called Ulchi-Freedom Guardian — that the United States and South Korea kicked off this week.
But Cheong Seong-chang, a senior analyst at the Sejong Institute in South Korea, said that the situation could deteriorate if the two sides persisted in "their confrontational posture in which one side's show of strength is matched by the other side's tough stance."
The Koreas are technically at war, the 1950-53 Korean War having ended with an armistice rather than a peace treaty.