South Korean officials said the incident involved the collapse of a 23-storey apartment building in Pyongyang's Pyongchon district, which already had close to 100 families in residence.
It is extremely unusual for the North to report negative news of this type, and its official KCNA news agency also reported equally rare apologies from top officials.
Leader Kim Jong-Un "sat up all night, feeling painful" after being told about the accident, the agency said.
An intensive operation had been mounted to rescue survivors and treat the wounded, it said.
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It did not give a figure for the number of dead or injured but said the accident left Pyongyang citizens "greatly shocked".
The agency carried lengthy public apologies by senior officials including the Minister of People's Security, Choe Pu-Il.
"(Choe) repented of himself, saying that he failed to find out factors that can put at risk the lives and properties of the people and to take thoroughgoing measures, thereby causing an unimaginable accident," it said.
"It is common in North Korea that people move into a new apartment building before construction officially ends," the official told AFP.
The official said 92 families were believed to be living in the collapsed building, and the final death toll was likely to be "considerable".
Among those making a public apology were Kim Su-Gil, chief secretary of the city committee of the ruling Workers' Party.