As the verbal confrontation grew between Trump and Kim, the North Korean central news agency released pictures that showed Kim inspecting the KPA Strategic Rocket Force's proposed plan, for launching ballistic missiles off the coast of Guam during on Monday.
The ministry quoted Mr Lavrov as saying tensions could rise again with the US and South Korea set to launch large-scale military exercises on Aug 21.
The U.S. and South Korean militaries next week are set to start their annual fall exercises, in which they practice responding to a North Korean invasion or the collapse of the regime in Pyongyang.
"He said that if the planned fire of power demonstration is carried out as the USA is going more reckless, it will be the most delightful historic moment when the Hwasong artillerymen will wring the windpipes of the Yankees and point daggers at their necks, underlining the need to be always ready for launching to go into action anytime once our Party decides", the report said.
The missile plans were previously announced.
Mr Kim said North Korea will conduct the planned missile launches if the "Yankees persist in their extremely risky reckless actions on the Korean Peninsula and its vicinity" and that the U.S. should "think reasonably and judge property" to avoid shame, the news agency said.
The Trump administration had no immediate comments on Kim's declaration.
US Secretary of State Rex Tillerson told reporters in Washington on Tuesday, "We continue to be interested in trying to find a way to get to dialogue, but that's up to (Mr Kim)".
Lobbing missiles toward Guam, a major US military hub in the Pacific, would be deeply provocative from the USA perspective. He has also warned, that the U.S. should think "reasonably" against its "recklessness". We do not seek an excuse to garrison USA troops north of the Demilitarized Zone.
South Korean Vice Defence Minister Suh Choo-suk highlighted doubts about North Korea's claims about its military capability. The small island strip in the Pacific is closer to the Korean peninsula than any other U.S. territory.
The US President had been told about a Washington Post article reporting on North Korea's ability to place miniature nuclear warheads on ballistic missiles when he fired off the comment last week.
Moon, in a televised speech Tuesday on the anniversary of World War II's end and the Korean Peninsula's liberation from Japanese colonial rule, said Seoul and Washington agree that the nuclear standoff should "absolutely be solved peacefully".
Mattis said that if a North Korean missile were headed toward the waters near Guam, instead of aimed directly at the island, then the president would decide what action to take.
After the meeting, Moon's spokesman said the president had "denounced" North Korea for disturbing the peace in the region with its repeated missile launches.
He said his South Korean government "will put everything on the line to prevent another war in the Korean Peninsula".
Speaking at a meeting of his senior advisers Monday, South Korean President Moon Jae-in echoed the call for Pyongyang to make the "correct choice".
Pentagon officials have told Fox News that the US military stands ready to "fight tonight".
Seoul, a vibrant metropolitan area of 25 million people, lies within range of North Korea's conventional artillery, stationed just across the border 30 miles to the north. Hundreds of thousands of Americans, including more than 28,000 US troops, also live in South Korea.
Mattis added that if North Korea fires at the USA, "it could escalate into war very quickly. yes, that's called war, if they shoot at us". It would be a test of the Hwasong-12, a new missile the country flight-tested for the first time in May. The liquid-fuel missile is created to be fired from road mobile launchers and has been previously described by North Korea as built for attacking Alaska and Hawaii.
Tensions have been mounting since the North tested two intercontinental ballistic missiles last month, which appeared to bring much of the U.S. within range.
The North's latest report said Kim ordered his military to be prepared to launch the missiles toward Guam at any time. If the "planned fire of power demonstration" is carried out because of US recklessness, Kim said it will be "the most delightful historic moment when the Hwasong artillerymen will wring the windpipes of the Yankees and point daggers at their necks", the news agency reported.