Scaled-down military drill comes after Pyongyang tested a series of short-range projectiles in recent weeks.
North Korea has threatened to carry out more weapons tests after it fired its fourth set of projectiles in less than two weeks following the start of joint exercises between the United States and South Korea.
The statement comes just an hour after the North fired on Tuesday “two projectiles that are assumed to be short-range ballistic missiles” from South Hwanghae province on its west coast.
The missiles flew about 450km across the peninsula and into the East Sea, also known as the Sea of Japan, reaching an altitude of 37km and a speed of “at least Mach 6.9”, South Korea’s Joint Chiefs of Staff (JCS) said in a statement.
Pyongyang said the combined military drills being carried out by South Korea and the US were a “flagrant violation” of the process.
North’s foreign ministry said the drills, which Pyongyang sees as an invasion rehearsal, leave the country “compelled to develop, test and deploy the powerful physical means essential for national defence”.
Trump has played down the tests by saying they did not break any agreement he had with Kim but the talks have yet to resume.
Analysts believe the tests are designed to improve North Korean military capabilities and to pressure Washington to offer more concessions.
A senior Trump administration official said: “We continue to monitor the situation and are consulting closely with our South Korean and Japanese allies.”
In Seoul, South Korea’s defence minister and the heads of the National Security Office and the National Intelligence Agency were meeting to discuss the latest firing of short-range projectiles, Ko Min-jung, a spokeswoman for the presidential office, said on Tuesday.
A North Korean foreign ministry spokesman said in a statement released through state news agency KCNA that North Korea remains committed to resolving issues through dialogue.
However, Pyongyang “will be compelled to seek a new road as we have already indicated” if South Korea and the US continue with hostile military moves, he said.
The arrival of new, US-made F-35A stealth fighters in South Korea, the visit of a US nuclear-powered submarine to a South Korean port, and US tests of ballistic missiles are among the steps that have forced North Korea to continue its own weapons development, the spokesman said.
“The US and South Korean authorities remain outwardly talkative about dialogue,” he said. “But when they sit back, they sharpen a sword to do us harm.”
North Korea has repeatedly complained that the US and South Korea’s joint military drills violate a pledge made by Trump to Kim.
South Korean media reported that the joint military exercises had started on Monday.
The latest launch also comes as a United Nations report said on Monday that Pyongyang has “continued to enhance its nuclear and missile programmes” and used cyberattacks to take in $2bn to fund the development.
The testing of short-range missiles by North Korea is covered by a 2006 UN Security Council resolution demanding that Pyongyang suspend all activities related to its ballistic missile programme.
Short-range missiles pose no threat to US territory but do put at risk its allies Japan and South Korea and the tens of thousands of US troops stationed in both countries.
Meanwhile, Japanese Defence Minister Takeshi Iwaya told reporters in Tokyo that Japan will respond “firmly” to the latest threat.
“North Korea’s attempt to upgrade its missile capabilities is a serious problem, not only to our country alone but to the entire region and we’ll be thorough in surveillance and steadily develop a comprehensive missile defence system.
“Even short and medium-range missiles are a serious threat to Japan. So we want to respond firmly as the Ministry of Defence,” he added.