More than 1,000 prisoners are refusing to eat in protest over poor conditions and the Israeli policy of detention without trial.
Other demands include increased family visits, improved medical care and the end of the use of isolation of prisoners.
The hunger strikers are drinking water and are taking twists of salt to stop their bodies from shutting down.
The strike began on 17 April and is being led by Fatah leader, Marwan Barghouti.
He is the most high-profile Palestinian prisoner in an Israeli jail.
According to recent polls, many Palestinians would like him to be their next leader.
He is often compared by Palestinians to the late South African President Nelson Mandela.
But for Israel, Barghouti is a terrorist.
He is the former head of Tanzim, the armed wing of the Fatah party which controls the West Bank.
Barghouti was one of the leaders of the second intifada and helped to organise the initial outbreak of violence in 2000.
In 2002 he was found guilty by an Israeli court of orchestrating attacks that killed five people. He is currently serving multiple life terms.
Barghouti did not mount a defence during his trial and refused to recognise the court’s authority.
The hunger strike presents a growing problem for Israel.
Barghouti’s role in the protest appears to be cementing his reputation as a man who will be difficult to ignore.
Many Palestinians hope Israel will one day have to release him because he is viewed by them as a unifying figure and a hero of the resistance.
Israel, though, has said it will not negotiate with “terrorists”.
But the longer the hunger strike goes on the greater the potential it has to fuel unrest in the Palestinian territories.
Barghouti’s son, Qassam, denied that the strike was timed to coincide with the anniversary of 50 years of Israeli occupation.
Israel captured the West Bank and Gaza during the June 1967 six-day war.
But in an interview with Sky News, he warned Israel that there would be consequences if the prisoners’ demands were ignored and their health deteriorated.
“When it comes to the prisoners issue there is no time – there’s no time for anybody to wait while we are talking,” he said.
“Now, any minute, we can hear the news that one of the prisoners might just pass out and that’s it – and after that who can control the Palestinian people?”
Israel, though, claims the hunger strike has nothing to do with the conditions in its prisons, which it says meet international standards.
Officials claim the strike is politically motivated and Barghouti is using it to improve his position, jockeying to be a possible successor to Mahmoud Abbas, the 82-year-old Palestinian leader.
Earlier this week, Israel’s prison service released footage to illustrate their point.
It claims the video shows Barghouti eating in his cell on two occasions in late April and May – unwrapping sweets and biscuits and sneakily consuming them in the toilet of his cell.
Israel’s security minister, Gilad Erdan, claims Barghouti is exploiting the strike for his own ends.
“This strike was never about the conditions of the convicted terrorist – their conditions meet international standards and law. It is only about Marwan Barghouti’s desire to gain political power and position himself to replace Abu Mazen.
“He lied to the Palestinian public when he claimed to be striking.
“Israel will not give in to extortion and pressure from terrorists.”
Barghouti’s wife, Fadwa, has denounced the video, claiming it was “fabricated” and is part of an Israeli strategy to discredit her husband.
Palestinian hunger strikes are not new, but this is the first mass strike in years.
Israel says it currently has 6,177 Palestinian prisoners held on terrorism-related charges in its jails.
Palestinian officials claim 800,000 Palestinians, about 20% of the population, have been imprisoned by Israel at one time or another since 1967.