The letter says Congress and the American people would hold Trump responsible if a "careless or ill-advised miscalculation" results in conflict that endangers USA military members or allies in the region.
"President Trump has basically drawn a red line".
The letter comes amid news that North Korea declared a plan to launch a ballistic missiles toward the US territory of Guam - 4,000 miles west of Hawaii in the Pacific - where the USA has a significant military presence.
Experts were quick to push back on the president's tweet, saying the US's nuclear arsenal hasn't actually changed much in the six months since Trump took office.
Trump also warned if Kim followed through on plans to strike Guam, the US response "will be an event the likes of which nobody's seen before".
Washington has warned it is ready to use force if needed to stop North Korea's ballistic missile and nuclear programmes but that it prefers global diplomatic action, including sanctions.
Pyongyang says its intercontinental ballistic missiles (ICBMs) are a legitimate means of defence against perceived United States hostility, including joint military drills with South Korea.
Mattis' words, some of the strongest he has issued on North Korea, followed incendiary comments from President Donald Trump who said on Tuesday that threats to the United States from Pyongyang would be met with "fire and fury".
Japan and South Korea vowed a strong reaction if the North were to go through with the plan.
Trump wrote in an early morning tweet: "My first order as President was to renovate and modernize our nuclear arsenal".
Tillerson spoke to reporters Wednesday after President Donald Trump and North Korea traded escalating threats of "fire", with the North saying it was examining plans for attacking Guam.
"The congresswoman agrees with Senator Humphrey that the Trump presidency has veered far off the rails", a spokesperson for Shea-Porter said, according to the Union Leader.
On Monday, two US B-1 bombers flew from Guam over the Korean peninsula as part of its "continuous bomber presence", a United States official said, in a sign of the island's strategic importance. In the memorandum, Trump directed the secretary of defense to initiate a new review.