Raafat Hamdouna, a Fatah representative, echoed his call, saying the two sides "must put aside anything that can harm our unity", the AFP news agency reported.
They were joined by international activists and relatives of detainees who gathered across Gaza, the occupied West Bank and East Jerusalem to honour the prisoners.
Nearly 1,000 people took to the streets in the West Bank city of Ramallah, carrying Palestinian flags and framed pictures of their loved ones held in Israeli jails.
More than 7,000 Palestinians, including 270 who are under the age of 18, are estimated to be currently held in Israeli prisons, the Palestinian Central Bureau of Statistics (PCBS) said.
Three of the prisoners have been in jail for more than 30 years, while 315have been detained for more than 15 years, it said in a statement.
An estimated 9,000 Palestinians are detained every year by Israel for either armed resistance or acts of civil disobedience and human rights groups say up to 700 teenagers and children were detained last year alone.
Al Jazeera's Nour Odeh, reporting from Ramallah, said human rights groups have warned that child detentions are on the rise, with some Palestinian youth reporting instances of abuse while imprisoned.
"Little is known about the long-term effect of detention on Palestinian children," she said.
"But with over a quarter million Palestinians imprisoned by Israel since 1967, experts say detention is a source of trans-generational trauma in Palestine."
The Israeli army refused to comment to Al Jazeera on whether the military is investigating allegations of child torture in its prisons.
"The IDF deeply regrets the cynical use of children by terrorist organisations who introduce them to terror and violence. As for the investigation, the IDF does not comment on its actions."