The action is being led by Marwan Barghouti, a Palestinian leader jailed by Israel for life for five murders.
Barghouti has been touted as a possible future successor to Palestinian Authority President Mahmoud Abbas.
Israeli authorities have placed him under solitary confinement for calling the strike - now in its second day.
Barghouti was "instigating mutiny and leading the hunger strike and that is a severe violation of the rules of the prison," said Israeli Public Security Minister Gilad Erdan.
"We have no reason to negotiate," Mr Erdan told Israeli public radio.
"They are terrorists and incarcerated murderers who are getting what they deserve," he added.
Protests in support of the prisoners were held in the occupied West Bank on the first day of the strike on Monday, with youths clashing with Israeli security forces in Bethlehem.
There are fears that the hunger strike - observed by 1,187 detainees, according to Israel's prison service - could fuel tensions across the Palestinian areas.
The issue of Palestinians held in Israeli jails is an ongoing source of tension between the two sides.
Palestinians regard the detainees as political prisoners. Many have been convicted of attacks against Israelis and other offences.
Others are detained under so-called Administrative Detention, which allows suspects to be held without charge for six-month intervals.
There were about 7,000 Palestinians held in Israeli jails at the end of last year, according to Palestinian prisoners' groups.
Barghouti (pictured in the poster) is among 7,000 Palestinians held in Israeli jails