Tours to the area were halted in 2008 after a North Korean soldier shot and killed a South Korean tourist.
The South has demanded a joint investigation into the death.
Tensions between the two sides were high after a South Korean warship sank near a disputed sea border after an explosion, killing 46 sailors.
Seoul has still not officially confirmed the cause of the blast, but a South Korean intelligence report apparently leaked to local media has said that it was almost certainly caused by a torpedo.
"It's our military intelligence's assessment that North Korean sumbmarines attacked the ship with a heavy torpedo," the Yonhap news agency quoted the report as saying.
Pyongyang has denied it was involved and on Friday said that South Korea was "crying out for the total severance of the North-South relations" by "deliberately" linking the sinking to the North.
Tours to Mount Kumgang began more than 10 years ago as part of reconciliation efforts between the two sides.
The resort provided much needed income to the impoverished country, but the North Korean state agency in charge of tours said in a statement published by state media on Friday that tours were unlikely to resume soon.
"The situation has reached such extreme phase that it is at the crossroads of a war or peace, much less thinking of the resumption of the tour," it said.
"It is quite natural that we can no longer show generosity and tolerance to the south side under this situation," the statement said.
Relations between the two Koreas, who are still technically at war, have been increasingly hostile since Lee Myung-bak became president of the south two years ago.
Earlier this week, Lee, who ended years of generous aid to the North, criticised Pyongyang for spending millions of dollars on a huge fireworks display to mark the birth of Kim Il-sung, North Korea's founder, suggesting the money would be better spent on feeding the population.