"Maoists poised for landslide win," declared a headline in the Himalayan Times daily.
Complete results are expected around April 20 at the earliest as counting is slow and the election was a complex mixture of direct and proportional systems.
Nepal voted for 601-member assembly, meant to write a new constitution for the impoverished Himalayan nation, formally end a 240-year-old monarchy, and make laws.
While 240 seats will be filled on a first-past-the-post basis, another 335 will be decided by proportional representation and 26 nominated by the cabinet.
The Maoists, once considered close to Peru's Shining Path guerrillas, now have abandoned the language of Marx and Mao. They have not called for nationalisation and say foreign investment is welcome in some sectors of the economy. They also favour land reform and social efforts to eradicate poverty.
"We urge every one not to doubt our commitment to multi-party competition," said Maoist chief Prachanda, after being declared a winner on Saturday.
The United States still considers the Maoists as terrorists. The result will also be hard to stomach for giant neighbour India, which is worried it may encourage its own Maoist insurgency, and Nepal's conservative army which had been resisting absorbing Maoist fighters into its ranks.
The election, and the abolition of the monarchy, had been the main demands of the Maoists during their decade-long insurgency, in which more than 13,000 people died.
Some analysts said the Maoists and mainstream political parties had set "peace, democracy and economic prosperity" as common post-conflict agenda for one of the world's poorest countries.
"The people have recognised the Maoists as main agents for these goals," said Yubaraj Ghimire, editor of the news magazine, Samay.
King Gyanendra, who stands to lose the most from the vote, also said he was satisfied with the "enthusiastic" participation of the voters.
