In a statement the NGO said the hunger strike, which began on Monday, had grown rapidly, with 250 prisoners joining on Tuesday.
The statement said the protests had spread to multiple Israeli prisons and had the backing of all major Palestinian political factions.
An official at the Israel Prison Service said he was aware of only 50 people refusing food at the Rimonim prison in central Israel.
The prisoners are calling for improved conditions in Israeli jails.
Islamist group Hamas in particular has objected to new electronic jammers installed in some of the prisons, intended to block cellphone reception.
The prisoners' club said indirect negotiations had begun.
Palestinian prisoners have regularly used hunger strikes to highlight their plight but this could be the largest since April 2017, when some 800 people refused food.
That protest ended a month later after negotiations.
The latest hunger strike coincided with fiercely contested Israeli general elections on Tuesday.
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