The former communist rebels held a comfortable lead with more than two-thirds of the 240 directly-elected seats allocated, election officials said.
Chandra Prakash Gajurel, a senior Maoist member, said: "We were partially surprised by the result."
"We knew we had good support from the people, but we had not imagined the victory on this scale.
"The country is heading towards the new system," Gajurel said.
"The biggest challenge could come from regressive forces who could try to disrupt the internal security situation."
The results released so far show the Maoists' rivals trailing - although Gajurel said the ex-rebels would "try to work together with other parties to form a coalition government".
In Kathmandu, the capital, hundreds of Maoist supporters have been celebrating each constituency win - chanting slogans and waving flags.
|Maoists carry flags bearing a hammer|
and sickle after their party's success[AFP]
The April 10 elections were a central part of a 2006 peace deal under which the Maoists agreed to end a decade-long civil war that had left at least 13,000 people dead.
The Maoists agreed to enter mainstream, multi-party politics, although the US still labels them as a "terrorist" organisation.
Nepal's largest and oldest party, the centrist Nepali Congress, had won just 30 seats and was leading in five others by Monday's tally, the election commission said, while the centre-left Communist Party of Nepal (Unified Marxist-Leninist) had won 24 seats and was leading in the count for nine others.
Other parties had won or were on track to win 32 seats.
The Maoists are pushing for the removal of Gyanendra, something that now looks certain following their success at the ballot box.
King Gyanendra ascended the throne after a palace shooting in 2001 - in which the former king and much of the rest of the royal family were shot dead at a party by one of the princes.
The monarch's status sank in 2005 when he fired the government and seized absolute power to fight the Maoists - only to push mainstream parties into the arms of the rebels and enter a peace deal that led to Thursday's poll.
Of the 601 seats in a new constituent assembly, 240 are appointed on a first-past-the-post system, and it is those results that are being tallied.
Some repolling will take place this week due to election day irregularities, with final results expected on April 22, Laxman Bhattarai, election commission spokesman, said.
Another 335 assembly members will be elected by proportional representation - a counting method the Maoists are also expected to do well in.
It could be several weeks before the full results for those seats are known.
The final 26 seats will be appointed by an interim government to be formed after the polls, which the Maoists can be expected to dominate.