He also slammed the travel ban as a "childish" and "vile" measure to limit people-to-to people contact.
Washington's State Department has declared USA passports invalid for travel to, in or through North Korea.
US passport holders will no longer be able to visit North Korea as tourists starting September 1, according to the State Department.
"Persons now in North Korea on a U.S. passport should depart North Korea before the travel restriction enters into effect on Friday, September 1st, 2017", the U.S. Department of State said.
American student Otto Warmbier, sentenced last year to 15 years' hard labour in North Korea, returned to the United States in a coma on June 13 after being released on humanitarian grounds, and died June 19.
The KCNA did not name Warmbier in Friday's report, but said the North had delivered "just punishment" to some U.S. citizens who had carried out acts against the regime.
The administration made a decision to ban USA passport holders from traveling to the DPRK based on concerns over "imminent danger to the physical safety", according to a notice by the State Department.
Maltrattamenti in casa di riposo, arresti e denunce: "Negavano acqua agli anziani"
Nuovo episodio di maltrattamenti ai danni di anziani in casa di riposo. Le tre arrestate sono G.L., 60 anni, L.S., 33 anni e M.S., 53 anni.
The North claimed that a sovereign state has a right to punish criminals under the law, defending itself against the angry reaction from the USA following Warmbier's death.
U.S. President Donald Trump also signed off on new sanctions against North Korea on Wednesday in response to human rights abuses and the repeated missile test launches.
Journalists, aid workers and individuals heading to North Korea to represent US national interests will be exempt.
Three American citizens remain detained in North Korea.
An article on Friday cited an unidentified Foreign Ministry official as saying global tourists had nothing to fear about going to North Korea, but defended the country's right to punish foreign criminals as it sees fit.
Washington has also said United States nationals who are resident in the country must have left by this date.
No details of how United States visitors might travel to the country in the circumstances were provided by the spokesman.