Election Commission official Bir Bahadur Rai said the counting started in several districts and that boxes filled with ballot papers had reached counting centers in at least 20 districts.
In the capital Katmandu, election officials opened ballot boxes collected from all 10 constituencies at the International Convention Center and began counting the thousands of ballot papers.
Rai said arrangements were being made to fly ballot boxes from some mountain areas by helicopter because snow had blocked roads. Nepal has 75 districts of which most of them are mountainous.
More than 70 percent of the 12 million eligible voters cast their votes during Tuesday's election in Nepal to choose the 601-member Constituent Assembly that would double as the parliament.
First results are expected by late Wednesday and final results are going to take at least a week.
The assembly will work on the long-delayed constitution. The last assembly elected in 2008 failed to fulfill the task because of squabbling among political leaders over who got to lead the nation. Some of the disagreements centered on whether to divide the country into a federal system based on ethnic groups or by geography.
The result was a power vacuum that has left Nepal without a proper constitution for nearly seven years.
Officials called the election successful and mostly free of violence. Although voting was suspended in one village.
A bomb exploded near a polling station in Katmandu injuring three people Tuesday. Opposition activists stormed a polling station in west Nepal village forcing police to open fire in the air.
The alliance of 33 opposition parties had vowed to disrupt the polls and declared a nine-day transport blockade. At least 30 people were injured in small bomb blasts and other violence in the run-up to the election.
The United Communist Party of Nepal (Maoist), the party of the former communist rebels, is hoping to repeat the last election and emerge as the largest party. Its main competitors are the Nepali Congress and Communist Party of Nepal (United Marxist Leninist).
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