Wednesday's explosions in the eastern city of Constatine continued the violent run-up to the vote after three suicide bomb attacks killed 33 people in the capital, Algiers, on April 11.
A police officer was killed and five other people were injured in the country's third-biggest city, Constantine, 48 hours after al-Qaeda called on Algerians to boycott the polls en masse.
There have been fears that the recent attacks will prompt a return to the levels of violence experienced in the 1990s.
The result was annulled after elections were won by the now banned Islamic Salvation Front.
The military then staged a coup and imposed a state of emergency that is still in place.
The ensuing fighting between rebels and government forces left more than 100,000 dead and missing.
Elections in Algeria were held again in 1997, but were marred by violence and fraud. It was known as the Bloody Decade.
Another election was held - it was also tainted by violence and the lowest voter turnout in Algerian history.
More than 18 million people eligible to vote in this round of elections as some Islamist groups call for a boycott.
The poll to choose the 389 members of the lower house of parliament is the third since a revolt follwed the cancellation of a national election in January 1992, which a now-outlawed party was poised to win.
Political analysts say that with power in Algeria concentrated in the hands of Abdelaziz Bouteflika, the president, whose mandate ends in 2009, many Algerians have little interest in parliament and may, therefore, not bother to vote anyway.
Algerians tend to believe the assembly exists to rubber stamp the decisions of the executive branch.
Social problems are Algerians' main concern, with unemployment among adults under 30 at 75 per cent.
The National Liberation Front (FLN), is expected to keep its position as the largest single party, with the pro-government Rally for National Democracy (RND) likely to take second place.
The FLN and RND are part of a ruling coalition with the Movement of Society for Peace (MSP).
Anwar Haddam, the former head of the Islamic Salvation Front (FIS), which had been posed to win elections in 1991 before they were cancelled by the military, said the low turnout reflected widespread dissatisfaction with the political system.
"The turnout was really low because people are fed up with all the rhetoric from the people who were involved in the coup-de-etat in 1991," he said.
Election results are expected to be announced on Friday.