The CPN-UML has so far bagged 42 seats in the elections.
Nepali Congress has won 38 seats while the UCPN (Maoist) was trailing behind with 8 seats, according to results declared.
Nepali Congress is leading in 66 constituencies, CPN-UML in 55 constituencies and UCPN-Maoist in 13 constituencies.
Top leaders who have been declared winners so far are -- CPN-UML leader and former Prime Minister Madhav Kumar Nepal who got elected from two constituencies and Unified CPN-Maoist Vice-chairman and former Prime Minister Baburam Bhattarai.
Nepali Congress President Sushil Koirala, senior leaders Sher Bahadur Deuba and Krishna Sitaula were declared winners in their respective constituencies.
President of Rastriya Prajatantra Party Pashupati Shumsher Rana lost election to CPN-UML candidate Sher Bahadur Tamang.
In Kathmandu's total 10 constituencies, Nepali Congress won seven and CPN-UML won three seats. Nepali Congress and CPN-UML have organised victory rallies at different places in the capital.
The counting will lead to the formation of a 601-member Constituent Assembly, including 240 elected under a direct voting system. Proportionate voting will elect members to 335 seats and the remaining 26 members will be nominated by the government.
Nepal's Maoists are threatening to boycott the newly-elected Constituent Assembly, alleging conspiracy.
The vote was only the second one since a civil war launched by Maoist rebels ended in 2006. Nepal was then transformed into a secular republic.
The country plunged into a constitutional crisis after the previous Constituent Assembly was dissolved without promulgating the Constitution last year, and fresh elections scheduled for November 2012 were not held.
With the formation of an election government led by Khil Raj Regmi in March, parties agreed after prolonged talks to conduct the polls in June or by December.
Political infighting, including a split in the ruling Maoist party last year, confounded efforts to implement a peace plan meant to rebuild Nepal after the 10-year civil war.