Communist Party of Nepal leader Prachanda, addressing an impromptu news conference, pledged to work with other parties to write a new constitution. ((Manish Swarup/Associated Press))

Nepal's Maoist former rebels have taken an early lead in an election for a new assembly, according to tallies from a vote held earlier in the week.

Election officials said on Saturday that candidates for the country's Maoist movement, the Communist Party of Nepal, have won 20 of about 40 constituencies where results from Thursday's vote have been declared, with one of the seats in the capital, Kathmandu, going to their leader Prachanda, who goes by one name.

Hundreds of Maoist supporters, many with faces painted red, celebrated the early wins by chanting slogans, and displaying the party's hammer and sickle symbol in the streets of the capital.

Prachanda himself appeared with red powder on his forehead and several garlands made from marigolds wrapped around his neck as he emerged from a counting centre, sounding like a winner.

"This victory is a command by the Nepali people to establish lasting peace," Prachanda told reporters. "We are fully committed to the peace process and multi-party democracy, and to rebuild this country."

"For the international community and especially our neighbours India and China, I want to say that our party wants good relations with all of them and is willing to work together on development cooperation and peace process," he added.

The election, Nepal's first in nine years, was aimed at cementing a peace deal that ended a decade-long civil war. Fighting during the Communist insurgency claimed 13,000 lives.

The rebels quit their armed struggle in 2006 and struck a peace deal with the government, following months of unrest that forced Nepal's king to cede absolute power.

The movement is still considered a terrorist group by the United States, but election observer and former U.S. president Jimmy Carter has said Washington must deal with the Maoists.

"It's been somewhat embarrassing to me and frustrating to see the United States refuse … 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," he told the BBC.