A 16-year-old boy was one of at least four people shot dead by police during a riot triggered by dissatisfaction over the election result in the restive province of Papua, an official said.

More than 300 supporters of a legislative candidate who claimed he should have won the seat in the local council attacked a district office in Asmat district.

The candidate, who was not identified, claimed based on the votes he should have won a seat in the city council but his name was replaced with another candidate's name.

The protesters, armed with sharp weapons, damaged the district office, local military spokesman Muhammad Aidi said.

Four soldiers guarding a nearby military post tried to control the protesters but were outnumbered, and one of the officers tried to control the mob by opening fire into the air, Aidi said.

"The mob became even more brutal and attacked the officer. In a such threatening situation another officer was forced to open fire and retreat to the post to save themselves," Aidi said in a statement Monday.

Four people, including the teenager, were shot dead while one more was injured and has been treated at a local hospital.

The military, local police and the human rights commission have formed a team to investigate the case, Aidi said.

Indonesia's presidential and legislative election also triggered a riot in the capital Jakarta.

Supporters of presidential candidate Prabowo Subianto have been protesting since the election result was announced last week in favour of incumbent president Joko Widodo.

Subianto's supporters claim the election was marred by rampant electoral fraud.

Since the riots began, more than 400 demonstrators have been arrested, according to police, who blamed the violence on "provocateurs" they claimed mixed with the crowd to stir up trouble.

Police said seven demonstrators have died but offered few details on how they died or who was responsible.

About 900 people were injured in the riots, according to the Jakarta Health Agency.