The warning is the latest of a string of threats by Kim Jon Un that have raised tensions on the Korean peninsula.
Analysts say a full-scale conflict is extremely unlikely, noting that the move would be suicidal for North Korea. But the North's continued threats toward Seoul and Washington, including a vow to launch a nuclear strike, have raised worries that a misjudgment between the sides could lead to a clash.
On Saturday, Caitlin Hayden, a spokeswoman for the White House National Security Council, said they're taking the North Korea's threats seriously. Hayden also noted the country's government has a long history of bellicose rhetoric and threats.
The country's threats are seen as efforts to provoke the new government in Seoul, led by President Park Geun-hye, to change its policies toward Pyongyang, and to win diplomatic talks with Washington that could get it more aid. North Korea's moves are also seen as ways to bolster the image of young leader Kim Jong Un in his country.
On Thursday, U.S. military officials revealed that two B-2 stealth bombers dropped dummy munitions on an uninhabited South Korean peninsula as part of annual defense drills that Pyongyang sees as rehearsals for invasion.
Hours later, Kim signed a rocket preparation plan and ordered his forces on standby to strike the U.S. mainland, South Korea, Guam and Hawaii.
North Korea said in a statement Saturday that all matters between the sides will be dealt with in a manner befitting war.
"Now that the revolutionary armed forces of the DPRK have entered into an actual military action, the inter-Korean relations have naturally entered the state of war," said the statement, which was carried by Pyongyang's official Korean Central News Agency, referring to the North's official name, the Democratic People's Republic of Korea.
Provocations "will not be limited to a local war, but develop into an all-out war, a nuclear war," the statement said.
South Korean Defense Ministry spokesman Kim Min-seok said his country is maintaining full military readiness to protect the public in response to the North's threats.
"The series of North Korean threats - announcing all-out war, scrapping the cease-fire agreement and the non-aggression agreement between the South and the North, cutting the military hotline, entering into combat posture No. 1 and entering a 'state of war' - are unacceptable and harm the peace and stability of the Korean Peninsula," Kim said."
Pyongyang also threatened to shut down the jointly run Kaesong industrial park, a border complex that's the last major symbol of inter-Korean cooperation.
Military leaders determined nearly 100,000 U.S. troops would be needed to storm the country and secure North Korea's nuclear material.
The Associated Press contributed to this report.
