(CNN) -- Seoul put South Korean forces on high alert and Pyongyang urged an increase in its "military capability" as the death of North Korea's enigmatic leader Kim Jong Il spurred fresh security concerns in the tense region.
A tearful state TV broadcaster reported Kim's death Monday. She said the 69-year-old leader died Saturday due to "overwork" while "dedicating his life to the people."
North Korea's official KCNA news agency said Kim suffered "great mental and physical strain" while on a train during a "field guidance tour." Kim, who had been treated for "cardiac and cerebrovascular diseases for a long period," suffered a heart attack on Saturday and couldn't be saved despite the use of "every possible first-aid measure," according to the agency.
In the country where Kim was revered as "dear leader," passers-by wept uncontrollably on the streets of Pyongyang.
"My leader, what will we do? It's too much! It's too much!" one person sobbed. "Leader, please come back ... You cannot leave us. We will always wait for you, Leader."
Kim's son, Kim Jong Un, will likely take over the reins. A letter from the ruling Workers' Party on Monday dubbed him "the great successor."
Kim's body will remain for a week at the Kumsusan Memorial Palace in Pyongyang -- where the body of his father Kim Il Song lies. Memorial services will follow on December 28 and 29.
"We should increase the country's military capability in every way to reliably safeguard the Korean socialist system and the gains of revolution," the National Funeral Committee said.
For its part, South Korea's National Police Agency ordered officers across the country to be ready for overtime shifts. President Lee Myung-bak canceled the rest of his Monday schedule, and all members of South Korea's military were placed on "emergency alert," his office said.
Under the alert -- which is short of the highest possible level -- South Korean forces will monitor North Korean troop movements closely and tighten security measures at sea, according to the ministry of defense.
Following the Korean War in 1950, the two nations never formally signed a peace treaty and remain technically at war -- separated by a tense demilitarized zone
"South Korea's concern is warranted, frankly, because an insecure North Korea could well be an even more dangerous North Korea," a U.S. official said.
But the demilitarized zone between the Koreas remained peaceful on Monday. And Lee asked South Koreans to focus on "economic activities" and remain calm.
"We have not seen any unusual movement ... from North Korea," said Choi Jong Kun, a professor at Yonsei University in Seoul. "We will have to watch and see."
U.S. President Barack Obama spoke with Lee early Monday morning and the two agreed to stay in "close touch as the situation develops," the White House said.
Kim Jong Il had been in power since 1994 when his father -- the nation's founder -- died of a heart attack at age 82.
The enigmatic leader was a frequent thorn in the side of neighboring South Korea, as well as the United States.
North Korea's nuclear program -- and international attempts to hinder its nuclear weaponry potential -- put Kim at odds with many world leaders in recent years, as did his governing style.
Under his leadership, North Korea was largely closed off to outside influences, fearful of threats from its neighbors. At the same time, it also sought international aid after extensive famines contributed to the deaths of tens of thousands of people.
Both North Korea and South Korea have shown signs of concession in recent years. Pyongyang has expressed willingness to engage with countries involved in multilateral talks aimed at North Korea's denuclearization, while Seoul recently sent humanitarian aid through U.N. agencies to help the malnourished population in the North.
But relations between the two rival nations soured yet again when the South accused the North of launching an attack on the South Korean island of Yeonpyeong. Two South Korean marines and two civilians were killed.
There have been reports in recent years about Kim's failing health. But North Korean news reports earlier this fall indicated that Kim had been traveling around the country and visiting China, a big change from 2009 when he was thought to be ill with cancer.
On Monday, the ruling Workers' Party announced what many experts had long assumed: Kim will be succeeded by his son, Kim Jong Un.
"Standing in the van of the Korean revolution at present is Kim Jong Un, great successor to the revolutionary cause of Juche and outstanding leader of our party, army and people," a party letter posted on the KCNA news agency said.. "Kim Jong Un's leadership provides a sure guarantee for creditably carrying to completion the revolutionary cause of Juche through generations."
The philosophy of "juche" or self-reliance is the basis of North Korea's reclusive nature.
"This has been in place for a while," said Mike Chinoy,