"We urge all parties to exercise maximum restraint and avoid confrontation," Dujarric stated, RIA Novosti reported.
The Spokesman added that UN officials had been in contact with interlocutors on both sides, emphasizing "the need to allow people to demonstrate peacefully."
The Gaza Health Ministry has reported that eight men were killed and more than thousand injured people were taken to hospitals and field clinics.
Local media estimated a turnout of about 20,000 protesters, less than the estimated 30,000 crowd size the previous Friday, when at least 20 were killed by Israeli gunfire and more than 1,000 injured. Palestinian officials plan to hold similar protests every Friday.