The Sushil Koirala-led Nepali Congress (NC) was leading in 72 constituencies while its rival CPN-UML was ahead in 55 seats.
The Unified CPN-Maoist was third, leading in 21 seats, according to the trends projected by the Nepalese media.
Results for the polls were also announced for 20 seats with both NC and CPN-UML sharing 10 seats each.
In what came as a double blow to Maoist supremo Prachanda, he and his daughter were handed down humiliating defeats in the polls.
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Nepali Congress candidate Rajan K C beat Unified CPN-Maoist chief, securing 20,392 votes and restricting Prachanda to 12,859 in his Kathmandu Constituency 10. Third candidate in contention CPN-UML's Surendra Manandhar also secured more votes than Prachanda (13,619 votes).
Prachanda is also contesting from Siraha Constituency 5, where he was leading the vote count.
In Kathmandu constituency No 1, Nepali Congress general secretary Prakash Man Singh won the election by defeating his nearest rival Renu Dahal, daughter of Prachanda, by a huge margin.
Meanwhile, Unified CPN-Maoist today demanded a suspension of the vote count, alleging conspiracy after initial results showed the party trailing at third position in the polls.
"Due to the conspiracy and unusual activities during the constituent assembly elections, counting did not go ahead as per people's expectations and opinions, therefore, we demand that the vote counting be postponed," the party said in a statement.