The party of Lesotho's prime minister was leading as initial results from general elections in the southern African nation were released.

The election commission said on Sunday that Prime Minister Thomas Thabane's All Basotho Convention party was ahead with wins in 35 out of 80 voting districts.

 Counting underway in Lesotho's snap election

Some supporters of his party, which performed well in the area of the capital, Maseru, took to the streets to celebrate the early results in the snap general election aimed at resolving a political crisis triggered by an alleged coup bid.

Tensions were high ahead of Saturday's parliamentary poll, which was called two years ahead of schedule, but election day passed off without incident, according to observers.

Al Jazeera's Erica Wood, reporting from the outskirts of Maseru, said that "Thabane's party did well even in constituencies that have traditionally voted for his rivals".

The Democratic Congress of Pakalitha Mosisili, a former prime minister, was second with 10 district victories in Saturday's election. The Lesotho Congress for Democracy, a party led by Mothetjoa Metsing, the prime minister's deputy, had won two.

'Peaceful election'

More results are expected on Monday morning.

The deputy president of neighbouring South Africa, Cyril Ramaphosa, said shortly after polls closed, "Everything I've come across tells me everything has gone extremely well.

"From my side it is congratulations to the people of Lesotho for having come this far to hold a peaceful election," Ramaphosa added.

The Independent Electoral Commission (IEC) also said the election had proceeded largely without incident, although some ballot papers in two of over 2,000 polling stations did not have the names of all candidates.

"In Lesotho, we don't count the votes electronically, we count them manually," said IEC official Rethabile Pholo.

According to local media, about 1.2 million people - out of a population of 2.2 million - were registered to vote.

Lesotho has been in crisis since June 2014, when Prime Minister Thabane suspended parliament to avoid a motion that would have seen him ousted from power after his fragile coalition government fell apart.

On August 30, soldiers attacked police headquarters, looting weapons and killing one officer.

Thabane described the violence as a coup attempt fuelled by the opposition and fled to neighbouring South Africa.

Both the military and opposition denied any bid to topple him. The army was confined to barracks during Saturday's vote.

Ramaphosa was appointed by the regional bloc Southern African Development Community (SADC) last year to try to broker an end to the deadlock.

Source: Al Jazeera and agencies