The detainees, held at Lakhal jail at Laayoun, the main town in Western Sahara, "began an indefinite hunger strike against inhuman practices despite their health conditions," their families said in a statement on Thursday.
The statement accused the authorities of putting the inmates under "psychological and physical pressures", barring their access to health care and isolating them from other detainees.
Five prisoners out of 37 who took part in the earlier hunger strike, begun on 8 August, are not fasting because they remain ill, the families said.
Concern for the prisoners' health during their previous hunger strike prompted human rights groups to urge the Rabat government to open dialogue with them.
Some had to be resuscitated in hospital after falling into unconsciousness before the fast was suspended.
The families said they feared inmates might die as a result of the new hunger strike and urged the authorities to meet their demands by improving their jail conditions and "respecting their rights as political prisoners".
"A humanitarian crime would take place if the prison authority does not shed its stubbornness and turns its back on the demands of our sons," their statement said.
Officials in Rabat were not immediately available for comment.
The government has repeatedly said that the prisoners, whom it describes as "supporters of separatism", enjoy rights as detainees including access to media and healthcare.
Morocco has said the previous hunger strike was a manoeuvre by the Polisario Front to deflect international criticism of its alleged abuses of prisoners of war.
The prisoners suspended that hunger strike after nearly two months at the end of September after Moroccan authorities promised to meet some of their demands, including the transfer to Lakhal prison of those held at other jails.
"A humanitarian crime would take place if the prison authority does not shed its stubbornness and turns its back on the demands of our sons"
The detainees' families
The prisoners also want Rabat to lift what they call its heavy security presence in Laayoun.
Most of the prisoners were jailed after anti-Moroccan riots in May. Many have been imprisoned for up to five years, for offences including sabotage of public property and use of weapons against public officials.
Western Sahara, which is rich in phosphates and fisheries and also may have offshore oil, is at the centre of a 30-year dispute between Morocco and the Algerian-backed Polisario Front independence movement.
Morocco, claiming centuries-old rights over the territory, annexed it after former colonial power Spain pulled out in 1975, triggering a low-level guerrilla war with the Polisario Front before a United Nations-sponsored ceasefire in 1991.
A UN peacekeeping mission has been trying to organise a
referendum on the territory's future ever since.