His statement asked the Nepalese people to pray for the 29-year-old prince's speedy recovery.
In a message to the people, he said only that the deaths had occurred after the sudden discharge or explosion of an automatic weapon inside the palace.
The prince regent did not say who was holding the gun at the time of the killings, nor why it went off.
New king in coma
The crown prince is now reported to be in a coma, but he has nonetheless been named king in keeping with Nepal's constitution.
Prince Gyanendra, his uncle, has been appointed regent.
His statement asked the Nepalese people to pray for the 29-year-old prince's speedy recovery.
It remains to be seen whether the prince's explanation of the deaths will satisfy a public experiencing both grief and anger.
The BBC's Daniel Lak, in Kathmandu, says the authorities are in a constitutional bind.
If they confirm that the new King was the man behind the massacre, he says the constitutional implications for both the monarchy and the country are dire.
Appeal for calm
Prime Minister Girija Prasad Koirala appealed for calm after Saturday's royal funerals, during which leading politicians were booed by sections of crowds who swarmed onto the streets of the capital, Kathmandu.
Tens of thousands lined the route of the funeral procession, as it wound its way for 12km (seven miles) through the city to the banks of the Bagmati river for cremation.
The loss of so many members of the royal family in such horrible circumstances, and the thought that the new king was involved in killing has added to the sense of crisis.
Public life will cease completely during the five-day mourning period now under way.
Security will have to be tight, due to fears that people might be more inclined to take part in unrest or violence while normal life is suspended.
It is expected that there will be a heavy police and possibly army presence in the streets of Nepal's cities in the coming days.