Leader Kim Jong-un guided exercises by nuclear tactical units over the past two weeks, North Korea's state news agency KCNA reported. These involved ballistic missiles with mock nuclear warheads and were meant to deliver a strong message of deterrence, it added.
The tests simulated striking military command centres, main ports and airports in the South, KCNA said.
"The effectiveness and practical combat capability of our nuclear combat force were fully demonstrated as it stands completely ready to hit and destroy targets at any time from any location," the KCNA report added.
"Even though the enemy continues to talk about dialogue and negotiations, we do not have anything to talk about nor do we feel the need to do so," KCNA quoted Mr Kim as saying.
The agency said North Korea's ruling Workers' Party decided to conduct the drills as an unavoidable response to a large-scale mobilisation of US and South Korean naval forces, including an aircraft carrier and a nuclear-powered submarine.
"The statement they've released is crystal clear that this recent spate of tests was their way of signalling resolve to the United States and South Korea as they carried out military activities of their own," said Ankit Panda of the Carnegie Endowment for International Peace, a US think tank.
Washington and Seoul held joint maritime exercises involving an American aircraft carrier on Friday, a day after the South scrambled fighter jets in reaction to an apparent North Korean aerial bombing drill.
The exercises involved the US carrier Ronald Reagan and its strike group. The naval forces of South Korea, Japan and the US also conducted joint drills before that.
After the North Korean statement on Monday, South Korean President Yoon Suk-yeol's office said "it is important to accurately recognise the severity of security issues in the Korean Peninsula and north-east Asia to prepare properly," an official was quoted as saying.
American-led UN forces are still technically at war with North Korea as the 1950-1953 Korean War ended in an armistice rather than a peace treaty.
North Korea had only referred to one missile as having a tactical nuclear capability, but the statement clarifies that many systems, new and old, will be assigned such a role, Mr Panda said.
If North Korea resumes nuclear testing, it could include development of smaller, tactical warheads meant for battlefield use and designed to fit on short-range missiles such as the ones tested recently, analysts said.
South Korean and US officials say there are signs North Korea could soon detonate a new nuclear device in underground tunnels at its Punggye-ri test site, which was officially closed in 2018.
Analysts say putting small warheads on short-range missiles could represent a dangerous change in the way North Korea deploys and plans to use nuclear weapons.
On October 4, the North test-fired a ballistic missile further than ever before, flying what it said was a new intermediate-range ballistic missile, or IRBM, over Japan for the first time since 2017.
Analysts confirmed that the photos released by state media showed a previously unseen IRBM.
"It's incredibly unusual, though, that they'd test a previously untested missile for the first time over Japan. It suggests a substantial degree of confidence in the engine," Mr Panda said.
Among the other missiles shown in the photos were short-range ballistic missiles that included KN-25 and KN-23 types as well as one with a heavy 2.5-tonne payload, as well as a KN-09 300mm multiple launch rocket system.
The photos notably showed a test of a "navalised" KN-23 designed to be launched from a submarine. That missile was revealed in a test in the ocean last year, but this time the test was conducted in a way that simulated a launch from what state media called "a silo under a reservoir".
This year, North Korea has test-fired missiles from different locations and launch platforms, including trains, in what analysts say is an effort to simulate a conflict and make it difficult for enemies to detect and destroy the missiles.
The KN-23 is designed to perform a “pull-up” manoeuvre as it approaches a target, intended to help it evade missile defences.