The UN has said media restrictions and violence meant the environment was not conducive to free, credible elections.
Unrest started in April after President Pierre Nkurunziza said he would run for a third term - something protesters say is illegal.
The president says he is entitled to a third term because he was appointed for his first term, not elected.
The presidential election is scheduled for 15 July. East African leaders have called for a further two-week delay.
Africa news highlights: 7 July
The electoral commission spokesman told the BBC turnout for the parliamentary poll had been low in the districts of Bujumbura where there had been protests, but that in some provinces outside the capital it was as high as 98%.
The ruling party - the CNDD FDD - was ahead in every province of the country, Burundi's electoral commission announced.
They won 77 out of 100 elected seats in parliament, AFP news agency says.
The BBC's Maud Jullien says all of the country's private broadcasters have closed in recent months, and many civil society leaders have left the country claiming their lives were under threat.
At least 70 died and 150,000 people have fled the country.
Reporting on a coup and a crisis... using a music-sharing site
10.4m population
50 years - life expectancy for a man
2nd poorest country in the world
85% are Hutu, 14% Tutsi
300,000 died in civil war
The ruling party in Burundi has won the parliamentary election boycotted by the main opposition parties.