Parties can submit the names of candidates chosen under the proportionate representation system by December 25, said a notice issued by Election Commission (EC) spokesperson Bir Bahadur Rai.
Nepal has a dual system of both directly-elected seats and members nominated through proportional representation.
Out of a total of 601 assembly seats, 335 have been allotted under the proportionate voting system and parties will get seats in proportion to votes they received in direct elections to 240 seats during the November 19 polls.
The CPN-UML with 175 seats secured second position, followed by the UCPN-Maoist with 80 seats.
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The Maoists, who swept Nepal's first post-war polls in 2008, asked for more time to consider their options and demanded an investigation into alleged poll-rigging.
They are expected to make a final decision on whether they will join the assembly by that date.
Parties were initially expected to submit lists of proposed lawmakers by December 10 but the EC extended the deadline till December 18.
The political parties will have three more weeks for forming a new government after the deadline to submit the names of the members of the Constituent Assembly ends.
The new government will nominate a further 26 members to the assembly, which will also function as a parliament and is expected to bring an end to the country's years of political instability.
Nepal has been facing a constitutional crisis for last five years after the first Constituent Assembly was dissolved without promulgating the Constitution last year.