Maoist supporters with their faces painted red celebrated
Nepal's Maoist party has taken the lead in results declared so far, after Thursday's elections.
The Maoists have won 14 out of 24 seats declared, and their leader has taken a seat in the capital, Kathmandu.
The party is also ahead in many other seats, for which partial results are coming through as the count proceeds.
The polls, for an assembly to re-write the constitution, are the first to test the Maoists at the ballot box after their 10-year guerrilla campaign.
The BBC's Charles Haviland says Maoist supporters in Kathmandu have started victory processions in some of the main streets, with red vermillion powder smeared on their faces and red hammer-and-sickle flags in their hands.
Although it is too soon to say the Maoists have won the election, there is a sense that the former guerrillas are doing better than most observers had expected, our correspondent says.
Nepal's two traditionally largest parties have gained only four seats each.
The Maoists' leader, Prachanda, called a press conference, where he called the results a "victory" and said he saw them as the people's mandate to consolidate peace.
"All eyes are upon us," he said.
The new constitution is expected to lead to the abolition of Nepal's monarchy, and the partial counts suggest small royalist parties have done badly in the polls.
One of the Maoist leaders who won in the capital, Pampha Bhusal, has said she will work hard to ensure the inclusion of women in all organs of the state, something our correspondent says would be a novelty in the Himalayan country.
The elections were Nepal's first since 1999
He told the BBC: "It's been somewhat embarrassing to me and frustrating to see the United States refuse among all the other nations in the world, including the United Nations, to deal with the Maoists, when they did make major steps away from combat and away from subversion into an attempt at least to play an equal role in a political society."
Mr Carter also talked about the significance of the elections:
"It's the end, I hope, of armed conflict, of revolutionary war in fact", he said.
Nepal held its first polls since 1999 following the Maoists' decision to quit their armed struggle in 2006.
Voting passed off relatively peacefully
Results for all the 240 constituencies are expected over the next 10 days. Officials say that polling has been postponed in 10 constituencies.
Many Nepalis and international observers have been surprised that Thursday's nationwide elections, just two years after the end of the Maoist insurgency, took place considerably more peacefully than past votes of the 1990s.
There were four election-related deaths in the troubled south-eastern region.
The Election Commission said there was a turnout of 60%, with polling cancelled due to malpractice in just 33 polling stations out of 21,000.
King Gyanendra seized absolute power in 2005 but was forced to give up his authoritarian rule the following year after weeks of pro-democracy protests.He has since lost all his powers and his command of the army.