Mohamed Boudarbala, 36, was found dead Friday in his cell in a new prison in the southern town of Archidona currently used as a so-called CIE -- a centre where migrants are held pending asylum claims after they arrive in Spain.
Police said an autopsy showed he hanged himself with a sheet, but an activist group and Boudarbala's brother have called for an independent probe after allegations of police brutality ahead of his death.
Algerian Justice Minister Tayeb Louh said prosecutors from the country were looking to "shed light on the circumstances of the suspicious death" last week in the detention centre, APS news agency reported.
His brother Ahmed Boudarbala denied Mohamed was suicidal.
"He was sporty, young, very happy and very positive. He died in murky circumstances," he told a news conference in Malaga this week.
Forty Algerian migrants who were detained alongside Boudarbala, were deported to their homeland on Wednesday accused of illegally entering Spain.
According to the International Organization for Migration, migrant arrivals by sea to Spain tripled in 2017 on the previous year, with some 21,500 people arriving.