Prime Minister Girija Prasad Koirala has appealed for calm.
The bodies of the royal couple and of several others were cremated amid scenes of near hysterical grief at a sacred Hindu site outside the capital, Kathmandu.
Under the constitution, the privy council has named Crown Prince Dipendra king, but he remains in a coma in hospital after turning the gun on himself. King Birendra's brother - Prince Gyanedra - has been appointed regent.
Prime Minister Girija Prasad Koirala has appealed for calm.
The cremation ceremony at the temple complex of Pashupatinath was awash with light from television cameras and the blazing funeral pyres of the royal family.
Hindu custom calls for cremations to take place as quickly as possible.
There were angry scenes during the funeral procession, especially when ministers from Nepal's elected government passed by grief-stricken crowds on the roadside.
"Shocking is an understatement, we have been orphaned by this loss," said a vegetable seller, Janardan Sharma, who like many in the capital had rushed to the royal palace early on Saturday to try to find out more news of the tragedy.
Many mourners shaved their heads and were going without salt in a traditional sign of Hindu mourning.
Police are out in force in the capital, but no major security problems have been reported.
The killings are the worst violence in the centuries-old history of the Himalayan kingdom's royal family.
Succession problems
Prince Dipendra, 29, shot his father, mother and most of his family at a banquet on Friday evening.
After first reports that the heir to the throne was also dead, medical sources said he was still alive, gravely ill and on life support.
The BBC's Daniel Lak, in Kathmandu, says this means that, whatever the circumstances, the constitution and royal tradition make Prince Dipendra first in line for the throne as the eldest son of a deceased king.
Prince Gyanendra is the senior of the late King Birendra's two younger brothers. He was away from Kathmandu at the time of the massacre.
Our correspondent says privy councillors and political leaders are thought to be anxious to name Prince Gyanendra as monarch and to try to resolve the crisis.
Monarchy has long been considered as the symbol of unity in the multi-ethnic and multi-cultural Himalayan kingdom.
National tragedy
Earlier on Saturday, Deputy Prime Minister Ram Chandra Paudel called the massacre "a national tragedy", and confirmed that the crown prince was to blame.
The king and queen's other two children - Prince Nirajan and Princess Shruti - are among the dead.
The murders are thought to be the worst mass killing of royalty since the Romanovs were put to death by order of Lenin in 1918 during the Russian civil war.
King Birendra, 55, ruled Nepal as an absolute monarch after ascending the throne in 1972, without political parties under a system of local panchayats or councils.
But nationwide unrest forced him to legalise political parties in 1990 and accept a parliamentary system.