Several dozens of Palestinian protesters blocked UN employees from entering the UN building in Ramallah on Wednesday, as they waved banners reading: "UNjust" and "UNfair."
More than a third of the 4,700 Palestinian prisoners being held by Israel are currently observing an open-ended hunger strike.
Two of them are marking their 71st day without eating in protest at their being held without charge under a procedure known as administrative detention which allows Israel to hold suspects indefinitely for renewable periods of up to six months.
Another five prisoners have been refusing food for between 48 and 66 days.
The vast majority began refusing food on 17 April to demand improved conditions, including increased access to lawyers and family visits, an end to solitary confinement and administrative detention.
Until now, Israel has rejected all appeals lodged by the hunger strikers, has refused them family visits and only briefly transferred one of them to a civilian hospital, sparking mounting protests from human rights groups as well as the UN.
"We note with disappointment your silence ever since this protest movement began in December 2011," protest organisers said in an open letter to Ban, referring to the month when a prisoner called Khader Adnan began a 66-day hunger strike which put the international spotlight on the issue of administrative detention.
Adnan ended his strike in mid-February after Israel agreed not to extend his detention. He was released on 17 April.
"This stands in stark contrast to your vocal and persistent remarks in support of formerly incarcerated Israeli soldier Gilad Shalit," they said, referring to a soldier who was held captive by Gaza's Hamas rulers for more than five years and released in October last year.
"We urge you to take a firm and vocal position in opposition to Israel's abuse and violation of Palestinian prisoners' rights," it said, demanding that the UN "encourage member states to stand against these gross human rights' violations."
The office of Robert Serry, the UN's Middle East envoy, had no immediate comment on the protest.
Last week, Serry issued a statement in which he said he was "deeply troubled" over the critical condition of the longest-running hunger strikers—Bilal Diab, 27, and Thaer Halahla, 33, and urged that a solution be found before it was "too late."
Meanwhile, Jamil Khatib, legal counsel for Diab, said his client had been transferred out of a civilian hospital and returned to the infirmary wing of Ramle prison near Tel Aviv on Monday, despite his chronic condition.
He also said Diab, Halahla and three others had begun refusing all intravenous liquids as well as any medical treatment from staff at the infirmary.
"Since yesterday (Tuesday), they have refused IVs and treatment from the prison staff as well as medical check-ups," he said.
"They are continuing their strike and are willing to continue until death. Their morale is high and they intend to stop drinking water soon," he warned.
On Tuesday, both the European Union and the Red Cross issued statements expressing concern about the plight of the longer-term hunger strikers and urged Israel to provide them with proper medical care.
Physicians for Human Rights-Israel also deplored Israel's refusal to allow the hunger strikers family visits.