Released in July 2017 after serving two years in prison for public order offences, Kamel Eddine Fekhar was re-arrested in late March for "attacks on institutions".
He was placed in detention in Ghardaia, some 480 kilometres south of the capital Algiers.
His lawyer Salah Dabouz said Fekhar died at the Blida hospital after being transferred there "in a comatose state".
The activist had been on hunger strike since he was detained, he told AFP.
In a video posted on his Facebook page, Dabouz denounced "this relentlessness and this planned death by the judicial authorities of Ghardaia" who detained Fekhar without reason.
Fekhar had been detained for weeks "in inhumane conditions", he added.
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He was first arrested in 2015 on the sidelines of ethnic violence in the M'zab valley, where Ghardaia is the largest city, between the country's Berber-speaking Mozabite minority and Chaamba Arabs.
"The authorities must immediately order an effective, independent and impartial investigation into the circumstances of his death and bring to justice anyone suspected of criminal responsibility," Amnesty International said.
The NGO said the authorities must also "immediately review their repressive policies and the shameful treatment of activists and protesters", adding that the country must allow for freedom of expression and the right to demonstrate peacefully.
Algeria's League for the Defence of Human Rights demanded justice and called for the "truth about the death" of Fekhar, describing him as a prisoner of conscience.
The Front of Socialist Forces, Algeria's oldest opposition group, called for a "full understanding of the circumstances" of the activist's death, which comes after "weeks of arbitrary and abusive detention".
Dabouz said he planned to lodge a complaint against local authorities for "failing to assist someone in danger", accusing the judiciary of letting Fekhar "die in prison".
In 2016, a British-Algerian journalist died while serving a two-year jail term for "offending" Algeria's president. Mohamed Tamalt's lawyer said he had lapsed into a coma after going on hunger strike.
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