Sunday's election was for seats in which the results in the November national election were annulled due to voting and counting violations.
The OSCE's Office for Democratic Institutions and Human Rights, which mounted a small observation mission for Sunday's elections, said in a statement that improvements included "a largely unimpeded campaign and increased opportunities for participation of domestic observers."
But it cited interference by local authorities in the election process and the composition of local election commissions as "issues of concern."
Azerbaijan's ruling party won five of the seats, while nominally independent candidates won three and opposition politicians took two.
The main opposition party Musavat, which failed to win any seats, alleged a "total falsification" of the results and called on international bodies such as the OSCE to take a more critical stance.
The November elections, as well as the tight restrictions on opposition gatherings to protest its outcome, raised concern in the West about President Ilham Aliev's commitment to democracy in Azerbaijan, which the West sees as a key source of oil and values for its strategic position bordering Russia and Iran.
The ruling party kept a majority in parliament in November's polls with the support of nominally independent lawmakers. The opposition alleged widespread irregularities.
Aliev came to power in flawed 2003 elections, succeeding his father, Geidar, a former KGB general who had been in power for a decade.
The troops of the Southern and Western military districts will begin to return from Russia's southern borders to the points of their permanent deployment starting April 23