The UN Security Council says its missile tests are "outrageous"
Kim Jong Un has ordered more missile tests and described the most recent launch as a "meaningful prelude" to containing Guam.
The North Korean leader's comments come as the United Nations met to discuss Tuesday's test of a ballistic missile designed to carry a nuclear payload over Japan.
Pyongyang's official Korean Central News Agency said it was a Hwasong-12 intermediate range missile that the North first successfully tested in May and threatened to fire into waters near Guam earlier this month.
Mr Kim was present for intermediate range missile launch over Japan.
He expressed "great satisfaction" over the launch which he called a "meaningful prelude" to containing Guam, which is home to key US military bases that North Korea finds threatening.
He said it is "necessary to positively push forward the work for putting the strategic force on a modern basis by conducting more ballistic rocket launching drills with the Pacific as a target in the future".
Following the launch US President Donald Trump said "all options are on the table".
"The world has received North Korea's latest message loud and clear: this regime has signalled its contempt for its neighbours, for all members of the United Nations, and for minimum standards of acceptable international behaviour.
"Threatening and destabilising actions only increase the North Korean regime's isolation in the region and among all nations of the world."
The UN Security Council strongly condemned North Korea's launch, calling its actions "outrageous" after an emergency meeting on the missile test.
"The Security Council, resolute in its commitment to a denuclearised Korean Peninsula, emphasises the vital importance of immediate, concrete actions by the DPRK to reduce tensions in the Korean Peninsula and beyond," the council said.
The council also said it was committed to a peaceful, diplomatic and political solution to the situation.
China and Russia's ambassadors to the UN said they opposed any unilateral sanctions on North Korea and reiterated calls to halt deployment of a US missile defence system in South Korea.
The US Ambassador to the UN is Nikki Haley: "The world is united against North Korea, there is no doubt about that.
"It is time for the North Korean regime to recognise the danger they are putting themselves in.
"The United States will not allow their lawlessness to continue, and the rest of the world is with us".
British Prime Minister Theresa May, meanwhile, has called on China to "do everything it can" to put more pressure on North Korea to stop "illegal" and "outrageous" missile tests.
Mrs May has landed in Japan for an official visit, one day after Pyongyang filed a missile over the north of the country.
Speaking to journalists on the flight, Mrs May said: "The actions of North Korea, of DPRK, are illegal. They are significant actions of provocation.
"I think it's outrageous. That's why we will be working with our international partners - as we have done previously but we will be doubling our efforts with our international partners to put pressure on North Korea to stop these illegal activities."
Mrs May, who says she spoke to President Xi Jinping about this issue at the G20 summit in Hamburg, added: "China has a key role to play here in terms of the pressure they can bring on North Korea."
She believes that Chinese pressure would be "the best way" of influencing North Korean leader Kim Jong Un. She added: "We would encourage China to do everything it can."
Officials in China, Pyongyang's only major ally, have urged all sides "to stick to peaceful and diplomatic means to resolve this issue".