Mattis' remarks came after Trump warned that 'appeasement' won't work with Pyongyang.
Trump and Kim had their historic first meeting in Singapore last June, wherein they agreed on denuclearisation of North Korea.
Kim's absences from official state media often spark speculation and rumors about his health.
A seismic tremor recorded in an area around North Korea's known nuclear site on Friday is suspected to be a nuclear test, says South Korea.
The United States has warned North Korea against going ahead with its long-range rocket launch and asked the international community to take appropriate actions to prevent Pyongyang from such a provocative act.
North Korea beat Japan 1-0 in a tempestuous World Cup qualifier on Tuesday, the result largely academic with the visiting Blue Samurai already through to the final qualifying round for 2014.
North Korea will take part in the next two Olympic Games in Japan and China, International Olympic Committee President Thomas Bach said on Saturday after meeting North Korean leader Kim Jong Un in Pyongyang.
The US Air Force B-1B Lancer bombers from Guam, along with the force's F-15C Eagle fighter escorts from Okinawa, Japan, flew in international airspace over the waters east of North Korea
The 15-member body strongly condemned North Korea's ballistic missile launches.
North Korea on Tuesday warned that it had the capability to launch a preemptive nuclear strike against the United States, "if necessary", following joint US-South Korea military drills earlier this week.
Tensions have dramatically risen on the Korean peninsula after North Korea early this month conducted its biggest nuclear test, which its state-run KCNA news agency described as a hydrogen bomb.
The State Department welcomed Germany's decision to downsize its diplomatic mission in Pyongyang and require North Korea to reduce its presence in Berlin.
The US president lauded the announcement on Twitter, writing "Great progress being made but sanctions will remain until an agreement is reached. Meeting being planned!"
There were reports that there was was dissent in the US President's regime over North Korea.
This test fire is the second time in less than a month and followed the sixth and most powerful nuclear test by North Korea to date on September 3.
South Korea Defense Ministry spokesman Kwon Ki-joon, said that "several projectiles" flew about 1,000 kilometers.
A defiant North Korea on Friday test-fired another short-range missile and warned of more 'self- defence counter-measures' if 'hypocrites' in the United Nations Security Council slapped sanctions on it for this week's nuclear test. North Korea launched a new type short-range missile with an estimated range of 160 km from its Musudan-ri rocket launch site on its east coast, a South Korean official said.
Asserting that the United States is ready with all its contingency plans to defend itself and its allies from any misadventure from North Korea, Defence Secretary Chuck Hagel has warned that the isolated nation was "skating very close to a dangerous line"."North Korea has been, with its bellicose rhetoric, with its actions, skating very close to a dangerous line," said Hagel with Army General Martin Dempsey, chairman of the Joint Chiefs of Staff.
Trump also said in a separate tweet that North Korea is 'no longer' the US' 'biggest and most dangerous problem', telling Americans and the rest of the world they can 'sleep well tonight!'
The two leaders spoke over phone to discuss the escalating tension after Kim threatened the US this week to fire missiles at Guam, a US island territory, after the US sponsored a resolution imposing new economic sanctions on Pyongyang over its missile and nuclear weapons programmes.
In the most recent show of force, Pyongyang put its military might on display during a parade on April 15 marking the 105th birth anniversary of the country's founder Kim Il Sung, grandfather of present ruler Kim Jong Un.
UN Secretary General Ban Ki-moon denounced the launch and asked North Korea to halt its 'provocative actions' and return to compliance with its international obligations.
The new sanctions imposed on North Korea by the United Nations Security Council would bite hard, US ambassador to the UN Susan Rice said on Thursday after the passage of an unanimous resolution in this regard.
Unless something changes, Mr Trump is a huge threat right now, which is perhaps not being recognised fully, cautions Debashis Basu.
India on Wednesday reacted strongly to the rocket launch by North Korea, saying the 'unwarranted action' by that country has adversely impact peace and stability in the Korean peninsula.
Trump told reporters that US and South Korea are facing the threat of reckless and brutal regime of North Korea.
India's top paddler prevailed over a tough field to win the singles title at the 21st Pyongyang Invitational tournament.
India remains North Korea's 2nd-largest import source after China, according to several estimates by multilateral bodies, says Subhayan Chakraborty.
The US president's remarks came in response to the latest ballistic missile test conducted by North Korea on Friday.
The projectile took off on Sunday afternoon local time from a location near Pukchang.
Kim said that his meeting with Moon would serve as a "historic chance" for the Korean people, who want to see the strengthening of inter-Korean relations.
North Korea on Wednesday test-fired a ballistic missile towards the Sea of Japan.
At the State Department after a meeting with the Foreign Minister of Turkey, Rice said she would not want to speculate on the motivations of North Korea over the missile tests or firings.
Trump's decision to call off the visit came just a day after Pompeo had announced that the newly appointed special representative for North Korea Steve Biegun and he will be travelling to North Korea next week to "make further diplomatic progress towards our objective."
His latest comments were less harsh than ones he made last month where he threatened "fire and fury" against the Pyongyang regime.
The disgraced scientist only helped North Korea in enriching uranium.
North Korea on Friday launched an ICBM for the second time in a month.
North Korea has abruptly cancelled United Nations Secretary General Ban Ki-moon's visit a day before he was due to arrive.
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