Foreign Minister Ri Yong Ho also says that his country has no intention of using nuclear weapons against any country "except the U.S".
Last month, the isolated regime defied a United Nations ban by testing ICBM's on America's July 4th holiday and again on July 28th.
Meanwhile, Chinese Foreign Minister Wang Yi yesterday said his country will pay the biggest price from the new United Nations sanctions against North Korea because of its close economic relationship with the country, but will always enforce the resolutions.
"Such military maneuvers of the USA may provoke a unsafe conflict under the present extremely acute situation prevailing on the Korean peninsula", said the Korean People's Army in a statement to the state-run news agency KCNA.
North Korea often commemorates significant events with stamps.
Tillerson also discussed the need to ramp up global pressure on North Korea to force it to abandon its nuclear weapons programmes in meetings with Australia, Japan and South Korea.
The United States-drafted resolution bans North Korean exports of coal, iron, iron ore, lead, lead ore and seafood. Both missiles were fired at highly lofted angles and analysts say the weapons could reach parts of the USA including Alaska, Los Angeles and Chicago if fired at a normal, flattened trajectory.
South Korea's government said that North Korea would face stronger sanctions if it does not stop its nuclear and missile provocation.
Russian Federation and China have the relatively closest diplomatic relations with North Korea.