Issa Qaraqe, head of prisoners affairs for the Palestinian Authority, said that "around 1 300 Palestinian prisoners" were participating in the hunger strike and the number could rise.
No injuries or damage were immediately reported as a result of the demonstrations.
The strike coincides with Palestinian Prisoners Day, which is usually marked on 17 April.
The umbrella body highlighted the deteriorating situation of those Palestinian prisoners who fall ill and are often neglected by the Israeli authorities.
The strike is led by Marwan Barghouti, a high-profile Fatah-linked prisoner, who is considered by some as a potential successor to President Mahmoud Abbas.
The Public Security Ministry said that the IPS would not conduct negotiations with the prisoners, in accordance with prison policy, and that all prisoners participating in a hunger strike will receive immediate disciplinary measures.
Palestinian president Mahmud Abbas, in a statement carried by official news agency WAFA, "called on the global community to save the life of the Palestinian prisoners in Israeli jails".
Fares says hundreds of prisoners launched a 28-day strike in 2012. "In the midst of this battle I call on all the Palestinian people and national institutions to show more solidarity so we can deliver the message of the prisoners to the whole world".
In recent years, previous Palestinian hunger strikers in Israeli custody have come close to death and had to be hospitalized.
Barghouti was arrested in 2002 during the violent Palestinian uprising and convicted on multiple counts of murder. The global community, it insisted, should bear its "legal and ethical responsibilities" to oblige Israel to respect worldwide law by dealing with the Palestinians it is holding as prisoners of war.
He promised that the new hunger strike "will demonstrate once more that the prisoners' movement is the compass that guides our struggle, the struggle for Freedom and Dignity, the name we have chosen for this new step in our long walk to freedom".
Palestinian leaders, including Prime Minister Rami Hamdallah and Palestinian Liberation Organization (PLO) Executive Committee Member Hanan Ashrawi, have backed the strike. He also called on the human rights institutions to compel Israel - the occupying state - to respect global law, as well as exposing Israel's violations of the law in its prisons.
"It is to be emphasised that the (prison service) does not negotiate with prisoners".
The prisoners' demands include more frequent family visits and easier access to telephones. "The delivery of mail is also limited and hardly takes place", he added.