Cambodia's King Norodom Sihanouk has confirmed he is determined to abdicate.
King Sihanouk's successor will be chosen by a nine-member council
In a letter read on radio and TV and posted on his website, he said he was too ill to continue.
His son, Prince Ranariddh, has travelled to Beijing, where the king is receiving medical treatment, to ask him to reconsider.
In his first public comments on the abdication, PM Hun Sen said lawmakers must work "day and night to prevent the country becoming a republic".
The prime minister said he had proposed King Sihanouk's other son, Norodom Sihamoni, to become the next king.
The deadline for picking a new monarch was 14 October, Hun Sen said.
Laws for deciding succession still not agreed
Nine-member throne council decides between candidates
King thought to want Prince Sihamoni to succeed
Eldest son Ranariddh says he does not want the post
On Friday, Cambodia approved a law on how to choose a new monarch which the senate and constitutional council still have to pass and which allows a nine-member Throne Council to elect Sihanouk's heir.
According to the new law, the council must meet within seven days to elect a successor if the king "dies, retires or abdicates".
"The hope that the king will retake his post as the king appears
to be lost," Hun Sen told reporters on his return from a summit of
Asian and European leaders in Vietnam.
Prince Ranariddh, who is also head of the national assembly, has said neither he nor his half-brother Prince Sihamoni want to take the throne in these circumstances.
Prince Sihamoni is a classically trained dancer and has worked in Paris for the UN's cultural organisation, Unesco. More recently, he has been with his father in China.
The king's decision shocked Cambodia, not least because the constitution, rewritten in 1993, does not cover the issue of abdication.
Most of the leading figures in Cambodian life have signed petitions asking the king to stay on.
In some quarters, the abdication announcement was seen as a move to spur Cambodia's political leaders to draw up plans for a succession, correspondents say.
The king, who turns 82 at the end of the month, has been receiving medical treatment in Beijing for several months for a "serious stomach complaint".
He says he will not return to Cambodia until a new monarch has been chosen.