He told military leaders North Korea would revise its military posture to be ready to launch pre-emptive strikes, the Korean Central News Agency said.
But despite its rhetoric it remains unclear how advanced the North's nuclear weapons programme is.
The UN has imposed some of its toughest ever sanctions on the North following its nuclear test and missile launch.
In response on Thursday, the North fired six short-range projectiles into the sea.
What impact will sanctions have?
Will carrots or sticks change North Korea?
KCNA said Mr Kim was speaking at a military exercise on Thursday, which is thought to be when the projectiles were fired.
He said North Korea "must always be ready to fire our nuclear warheads at any time" because enemies were threatening the North's survival.
"At an extreme time when the Americans... are urging war and disaster on other countries and people, the only way to defend our sovereignty and right to live is to bolster our nuclear capability," he was quoted as saying.
Analysts still doubt whether North Korea has the ability to make a nuclear bomb small enough to put on a feasible missile, but Kim Jong-un's announcement brought a swift response from the US.
"We urge North Korea to refrain from provocative actions that aggravate tensions and instead focus on fulfilling its international obligations and commitments," Pentagon spokesman Commander Bill Urban said.
The US and South Korea began talks on Friday on the possible deployment of a US missile defence shield in the South.
Initial talks will focus on the costs, effectiveness and environmental impact of installing the Terminal High Altitude Area Defense (THAAD) system, among other issues, the Yonhap news agency reported.
What is the Terminal High Altitude Area Defense System (Thaad)?
1. The enemy launches a missile
2. The Thaad radar system detects the launch, which is relayed to command and control
3. Thaad command and control instructs the launch of an interceptor missile
4. The interceptor missile is fired at the enemy projectile
5. The enemy projectile is destroyed in the terminal phase of flight
The launcher trucks can hold up to eight interceptor missiles.
Kim Jong-un has said North Korea's nuclear weapons should be ready for use "at any time", state media report.