The Nepali Congress (NC), its nearest rivals and election favourites before the vote, won a total of 110 seats, the election official said.
The Communist Party of Nepal (Unified Marxist-Leninist) - which before the polls was Nepal's second largest party - took 103 seats.
The Maoist party, called the Maoist Communist Party of Nepal (CPN-M) has said it plans to lead the government that will be formed from the assembly, but has appealed to its defeated rivals to join its members in a coalition government.
Malla said: "The parties have been asked to give the names of their candidates who will represent under the proportional representation seats within seven days."
Once the candidates have been put forward by the parties, it will take three days for the election commission to formally approve them.
But negotiations with the Nepali Congress and United Marxist-Leninist have so far yielded few results.
The two parties accuse the Maoists of widespread election irregularities, including beating up their supporters and blocking their candidates from campaigning and visiting polling stations.
Abolition of monarchy
Election rules dictate that once the lists of candidates have been approved, the first meeting of the constituent assembly has to be held within three weeks.
One of the assembly's first orders of business will be to remove King Gyanendra, Nepal's monarch.
The Maoists, supported by a number of other parties, have said the country's 240-year-old monarchy will be formally abolished as soon as the constitution-drafting assembly sits.
The elections earlier this month were a central strand of the 2006 peace deal struck between the former Maoist fighters and mainstream parties that ended a decade of civil war in which 13,000 people died.