King Gyanendra has given no sign he will step down willingly
The first meeting of Nepal's constituent assembly is to be held on 28 May, the government says.
According to the interim constitution, the assembly must abolish the monarchy on the first day it meets.
However one of the main parties is saying that the constitution must be amended first to clarify how much power the presidency will have.
Former Maoist rebels, now the biggest party in the government, have been urging King Gyanendra to step down.
They waged a civil war for 10 years, fighting for a communist republic, before signing a peace accord in 2006.
King Gyanendra seized absolute powers in February, 2005, saying the civilian government was failing in the fight with the Maoists.
The rebels and the main opposition parties then agreed on a programme to restore democracy.
In April 2006 the increasingly unpopular king agreed to reinstate parliament following weeks of violent strikes and protests against direct royal rule.
Last December, the Maoists and the other main political parties agreed that Nepal would become a republic after the elections to the constituent assembly, which were held in April.
Prime Minister Girija Prasad Koirala "has sent letters to all the participating political parties calling for the first meeting of the constituent assembly on 28 May," the prime minister's adviser Aditya Baral, told the AFP news agency on Monday.
Although the monarchy is supposed to end on the first day the constituent assembly meets, doubts grew on Monday as to whether that will happen.
The Maoists have been pushing for the monarchy to be replaced with a powerful presidency. And they want their leader, Prachanda, to be the first holder of the post.
However, a meeting of the Nepali Congress Party, the second biggest party in the country, says the interim constitution will have to be amended as there is no reference to the presidency or its powers in it.
Separately, former Prime Minister Krishna Prasad Battarai called for the monarchy to be kept, saying it was needed for national unity
The Maoists were the surprise winners of the April elections, taking nearly 30% of the votes.