The North's KCNA news agency, citing an unidentified spokesman for the foreign ministry, said there was no reason for foreigners to feel threatened while in North Korea and that citizens from around the world were encouraged to visit.
"Our doors are always open for all Americans who visit our country out of good will and wish to see our reality," the spokesman said.
The US State Department said earlier this week the ban would take effect on Sept 1, although some, including journalists and humanitarian workers, may apply for exceptions.
The ban will make reclusive North Korea the only country to which US citizens are banned from travelling.
It follows the death in June of US student Otto Warmbier, who was sentenced in North Korea last year to 15 years' hard labour for trying to steal an item bearing a propaganda item from his hotel.
Warmbier was in a coma when he was released by the North on humanitarian grounds and circumstances of his death remain unclear.
KCNA did not name Warmbier in Friday's report but said the North had delivered "just punishment" to some US citizens who had carried out acts against the regime.
North Korea is currently holding two Korean-American academics and a missionary in addition to a Canadian pastor and three South Korean nationals who were doing missionary work.
"There is no country in the world that would let foreigners who commit this sort of crime be," the spokesman said. "Ruling criminals by the law is exercising our confident right as a sovereign state."
The report said the ban reflects Washington's view of Pyongyang as an enemy and reiterated that President Donald Trump's administration should abandon its hostile policies towards the North.
Republican US Representative Joe Wilson, who introduced the bill to ban Americans from travelling to North Korea this year, has said hundreds of Americans are among the roughly 4,000 to 5,000 Western tourists who visit the North each year.
Aside from the threat of incarceration, North Korea's growing nuclear and missile threat is perhaps Trump's most serious security challenge.
The North test-launched an intercontinental ballistic missile last month that experts believe had the range to reach Alaska and Hawaii, and perhaps the US Pacific Northwest.
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