Donald Trump has given the go-ahead for South Korea and Japan to purchase a "substantially increased amount" of sophisticated military equipment from the United States as tensions with North Korea continue.

The US president made the announcement as the secretive state continues to perform nuclear missile tests, prompting outrage and concern worldwide for its "reckless and dangerous behaviour".

The US is said to be weighing up a number of responses to the North Korea missile crisis. The White House said Trump gave approval "in principle" to South Korean's president Moon Jae-in on 4 September to lifting previous restrictions and approving "many billions" in weapons sales to South Korea.

Ina tweet, Trump added: "I am allowing Japan & South Korea to buy a substantially increased amount of highly sophisticated military equipment from the United States."

Several other world leaders have responded to the ongoing concerns surrounding North Korea's nuclear missile capability.

German Chancellor Angela Merkel condemned the latest rounds of testing as a "flagrant violation" of international conventions but warned there should only be a "diplomatic and peaceful solution" to the crisis.

Russian President Vladimir Putin also warned against "military hysteria" with regards to the North Korea situation.

Speaking at a news conference in China, Putin stressed it was important for all parties, including North Korea, not to face "threats of annihilation" and "step on the path of cooperation".

He added: "Whipping up military hysteria makes absolutely no sense in this situation. This is a road to nowhere."

British Prime Minister Theresa May added the tests in North Korea area "reckless and unacceptable".

She added: "I discussed the serious and grave threat these dangerous and illegal actions present with President Abe in Japan this week and reiterate the call we jointly made for tougher action, including increasing the pace of implementation of existing sanctions and looking urgently in the UN Security Council at new measures.

"This is now even more pressing. The international community has universally condemned this test and must come together to continue to increase the pressure on North Korea's leaders to stop their destabilising actions."

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Donald Trump given the go-ahead for Japan and South Korea to buy more military equipment Alex Wong/Getty Images