He was making a rare public speech as part of mass celebrations involving troops, and military vehicles in Pyongyang to mark the 70th anniversary of the ruling Workers' Party.
Thousands of soldiers - many with red banners - marched past him through the city's main square in tight formation.
An aircraft flypast forming the number 70 flew over the square.
Tanks and missile carriers rolled past the podium where Mr Kim spoke.
Parade in pictures
At the scene: Steve Evans, BBC News, Pyongyang
The parade was truly amazing in its immensity and organisation. It lasted for two hours with countless rows of soldiers and then civilians marching past without break.
It felt at times like a meeting of a cult with citizens of North Korea jumping up and down and waving ecstatically at Kim Jong-un.
The message was clear from the podium:  China stands by North Korea - signalled by Kim Jong-un clutching the hand of a senior Chinese leader - and, secondly, that Mr Kim shows no sign of a softer stance towards the United States. As he put it:  "The party's revolutionary armament means we are ready to fight any kind of war waged by the US imperialists".
If his words were not clear enough, the hardware on parade underlined them - line upon line of trucks with missiles following line upon line of heavy artillery.
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State television carried the events live, adding an emotional commentary.
"Iron spirit and the united forces of our army and people have enabled us to break through the imperialists' sanctions and isolation, are forcing the enemies to extreme anxiety and fear," Mr Kim said.
Later, as the parade continued, tens of thousands of civilians, including school-children, danced and waved coloured pom-poms.
When it announced plans for the anniversary earlier this year, the government spoke of "cutting-edge" weaponry suitable for modern warfare, and the day's event will have been closely watched for any new military hardware indicating the North's military development.
No world leaders attended but China, North Korea's closest ally, sent a senior Communist Party official to the anniversary.
The North Korean leader began the day by paying respects to his late father and grandfather at the Kumsusan Palace of the Sun in Pyongyang, official media reported.
The celebrations continued, after a downpour of rain, with an evening torchlight parade which thousands of Pyongyang citizens have been seen practising for in public squares across the city.
A late-night concert featuring the all-female Moranbong Band - North Korea's most popular musical group - was also held, which cost foreigners wanting to attend about $115 (Â£75), the Associated Press news agency reports.
North Korea's nuclear programme has long been a cause for alarm in the region.
Pyongyang is believed to have conducted three underground nuclear tests and is threatening a fourth, despite international condemnation and sanctions.
Last month, it announced it was restarting its main nuclear facility Yongbyon and that it was improving its nuclear weapons "in quality and quantity".
The North claims it has made a nuclear device small enough to fit into the warhead of a missile.
US officials, however, have cast doubt on this claim and experts say it is difficult to assess the progress North Korea has made on miniaturisation.
North and South Korea remain technically at war because the 1950-1953 war ended in an armistice, not a peace treaty.
North Korea's supreme leader, Kim Jong-un, has said his country could defend itself in any war started by the US.