Bouteflika, in office since 1999, was hospitalized in Paris last year for three months after suffering a mini-stroke.
He is a candidate in the April 17 election despite concerns over his health, and is widely expected to win a fourth mandate, sparking rare criticism from senior political figures.
The demonstrators were rallying in response to a call from the "Rejection Front," a group made up of the families of missing persons from Algeria's civil war in the 1990s and members of an employment rights group.
"We are here to say that this election is nothing to do with us whatsoever. The people must have their say again," one protester said.
They carried placards reading "the people want to topple the regime," and chanted "the martyrs (from the civil war) freed the country, but the corrupt sold off its resources".
There was a heavy security presence at the central post office in Algiers, where the rally was taking place, and police encircled the protesters but did not otherwise intervene.
On Friday, thousands of people attended a government-authorized meeting in Algiers in favor of a boycott of the elections.
Previously, authorities had prevented all street demonstrations opposed to the election or Bouteflika's candidacy.
The election campaign begins on Sunday and will last until voting day.
BA/BA