They chanted slogans against the winner, ex-PM Abdelmadjid Tebboune, a former loyalist of ousted leader Abdelaziz Bouteflika.
Protesters are demanding that the whole political establishment be swept away.
Polling day itself was marred by protests and calls for people to boycott the election.
Mr Tebboune, 74, took 58% of the vote – enough to avoid a second round. But he and the four other candidates were criticised for being closely linked with the rule of Mr Bouteflika.
President Bouteflika stepped down following mass demonstrations across the country.
But anti-government rallies have continued since then unabated.
“The vote is rigged. Your elections are of no concern to us and your president will not govern us,” demonstrators chanted in central Algiers on Friday.
“Tebboune is worse than Bouteflika,” said one of the protesters, Meriem, a 31-year-old civil servant. “We did not vote and we will not back down.”