Ihsane El Kadi, director of the Maghreb Emergent news website and Radio M, was remanded in custody on December 29, four days after being detained.
On Monday, his lawyer said his detention had been extended on accusations of illegally collecting funds and acts that could "threaten state security."
El Kadi is suspected of "receiving sums of money and privileges from people and organizations inside the country and abroad in exchange for carrying out activities that could harm state security", the court said at the time.
Amnesty said the accusations against El Kadi in the North African nation were "trumped-up state security related offences".
"El Kadi's unjustified detention by the Algerian authorities... is yet another example of their ruthless campaign to silence voices of dissent through arbitrary detention and the closure of media outlets," said Amnesty's Amna Guellali.
He "must be released immediately and his two media outlets, sealed on 24 December, should be allowed to reopen," Amnesty said.
The headquarters of Interface Medias, which runs both news outlets, were also searched.
Last week, 16 international media figures including Russian journalist Dmitri Muratov, winner of the Nobel Peace Prize, called for his release and urged Algeria to lift "unacceptable" restrictions on his media.
Algeria ranks 134th out of 180 countries in RSF's 2022 World Press Freedom Index.