By Charles Haviland
BBC News, Kathmandu
Nepal's Prime Minister Girija Prasad Koirala says it would be good if King Gyanendra were to abdicate.
The king has been stripped of all his powers
He also says the unpopular crown prince should abandon his claim to the throne.
These are the most outspoken remarks against the monarch made to date by Mr Koirala who has always said he supports a ceremonial monarchy.
The king was forced to restore parliamentary democracy last April after weeks of street protests against his rule.
Since then, few Nepalese politicians from the ruling alliance will express so much as a word of support for the monarchy.
The veteran prime minister, Mr Koirala, has been an exception and last year was roundly condemned for saying he thought there should still be space for a ceremonial monarchy.
Popular protests swept Nepal last spring
But he has now shifted his ground, clearly in response to a controversial royal statement last month in which the king said his takeover of absolute power two years ago had been necessary.
Mr Koirala said this statement had made Nepal more likely to become a republic.
Saying the king and his son, Crown Prince Paras, had a "bad image", Mr Koirala said that it would be for the best, and would be internationally welcomed, if they abdicated their positions now.
It was not clear whether Mr Koirala was recommending the king hand power to his grandson, as some have urged.
But he said the abdications would put an end to the current chorus of demands, notably from the Maoist former rebels, that a republic be declared immediately.
Under last November's peace accord the future of the monarchy is supposed to be decided by an assembly elected later this year.
The king has already been stripped of all his political powers but has made two political statements since last April.
Generally he has kept a very low profile.
A recent opinion poll suggested more than half of Nepalis still want a monarchy of some kind, but most of the parties in the ruling coalition firmly support a republic.