The North conducted two nuclear test explosions and 24 ballistic missile tests in 2016, and experts predict it could have a nuclear-tipped missile capable of reaching the USA mainland within a few years.
The missile fired on Sunday blew up nearly immediately, the Pentagon said.
North Korea's deputy United Nations ambassador said a "thermonuclear war may break out at any moment", accusing the United States of escalating the situation in a news conference on Monday.
"If the USA is planning a military attack against us, we will react with a nuclear pre-emptive strike by our own style and method", Mr Han said.
A soldier films North Korean soldiers, officers and high ranking officials attending a military parade at the weekend.
Mr Mattis said Sunday's missile test had not involved an intercontinental ballistic missile but had still been reckless.
But US officials say expectations of an ambitious bilateral trade deal may be premature.
Since 2008, photographer Eric Lafforgue ventured to North Korea six times.
The "strategic patience" doctrine, which was used by the previous Barack Obama administration, hinged on the U.S. focusing on isolating North Korea by putting pressure on them through sanctions and waiting for them to denuclearise.
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Tensions have increasingly ratcheted up between North Korea and the United States in recent weeks.
How did we get here?
"That's a common failure mode for North Korean missiles very early on in their development cycle when they are working out the bugs in the propulsion and guidance system", the weapons expert told AFP. And by that I mean, if they can put a warhead on top of a missile that can reach the United States, that's obviously a direct threat.
US Vice President Mike Pence during his meeting with Japanese Prime Minister Shinzo Abe.
Meanwhile, China's once-thriving relationship with South Korea has hit the rocks over Beijing's strenuous objections to Seoul's deploying of an advanced US anti-missile system.
After 25 years of trying to deal patiently with North Korea over its nuclear programme, Pence said, "all options are on the table" to deal with a threat.
The department said there were still four North Koreans who had overstayed their work permits who had not surrendered, but their employers had said they would be handed over to authorities.
Noting Trump's recent military actions in Syria and Afghanistan, Pence said North Korea "would do well not to test his resolve" or the resolve of United States armed forces in the region.
"For Kim Jong-un to "behave" along the lines the USA demands would violate the North Korean culture - it would appear that Kim would be acting weak", said Mr Bennett.
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The US has military forces in South Korea on a permanent basis, and routinely threatens the North with military action. The meeting, scheduled to be chaired by Tillerson, will focus on North Korea's nuclear program.
"We'll be conducting more missile tests on a weekly, monthly and yearly basis", Vice Foreign Minister Han Song Ryol told BBC, adding that "all-out war" would occur if the USA took military action.
The system being installed in South Korea is created to shoot down missiles from North Korea or elsewhere.
At the United Nations on Monday, North Korea's permanent representative Ambassador Kim In-ryong, condemned the USA missile strikes in Syria, which targeted an air base after a suspected chemical attack by the government.
However, North Korea does not seem to be cowed.
And what about other world powers?
In Beijing, Chinese Foreign Minister Wang Yi made a fresh appeal for calm.
Pence's comments at the news conference elicited concern from Russia's foreign minister, Sergey Lavrov.
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