The Maoist party got the largest number of votes in the last election in 2008.
Chief Election Commissioner Neel Kantha Upreti said vote counting was continuing and there were no plans to stop it.
The Maoists are former communist rebels who fought government troops between 1996 and 2006. They gave up their armed revolt, joined a peace process and mainstream politics, and their fighters have joined the national army.
The Constituent Assembly, which was set up as part of the peace process, was first elected in 2008 but failed to complete the task of writing a new constitution.
Tuesday's election was to elect a new assembly to attempt again at writing a constitution.
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