Family of Majd Ziadeh, one of 1,500 hunger-striking prisoners, say they support the fight for dignity and humanity.
Dozens of Palestinians have been injured during protests in various parts of the West Bank, occupied since 1967 by the Israeli army, and near the security barrier that seals off the Gaza Strip.
The Israeli forces used tear gas, rubber bullets and live fire against thousands of protesters on Friday, the Palestine Red Crescent Society said.
About 1,500 people protested in Hebron, in the southern West Bank, while demonstrations also took place in other towns and villages.
The Palestinians were demonstrating in support of hundreds of prisoners in Israeli jails who have been on hunger strike since April 17, demanding better conditions.
In Gaza, which has been under a rigorous Israeli blockade for more than 10 years, hundreds of people waving Palestinian flags approached the concrete and metal barrier that separates it from Israel and threw stones and burned tyres.
The health authorities in Gaza said eight people were wounded by bullets and about 30 suffered the effects of tear gas inhalation.