The broadcast quoted army sources as saying that they had detained leading figures from Hamas and some from the Islamic Jihad, another Palestinian faction.
The sources linked the detentions to the disappearance of three teenage Zionist settlers who went missing late Thursday in the southern West Bank.
Zionist army cordoned off the West Bank city of Hebron as part of search efforts for the three Jewish teenage settlers.
'Israel Radio' said that the move was ordered by Defense Minister Moshe Ya'alon.
The Zionist army suspects that the three settlers are still in the Hebron area.
"In efforts to return the 3 abducted teens, Israel Defense Forces detained approximately 80 Palestinian suspects in overnight operations," Zionist army spokesman Peter Lerner wrote on his Twitter account on Sunday.
A leading Hamas figure told media outlets that the latest detentions included former ministers, lawmakers and mosque preachers.
The independent Ahrar Center for Prisoners and Human Rights, meanwhile, denounced the Zionist detentions.
In a statement, it said the detained Hamas leaders included MP Hassan Youssef, former prisoners affairs minister Wasfi Kabha and former minister Khalid Abu Arafa.
The center added that Zionist forces had re-detained at least 23 of the recently-referred Palestinian prisoners.
Occupation authorities also closed down the Gaza Strip's only functioning commercial crossing, Karam Abu Salem, starting Sunday and until further notice.
The closure was part of a series of punitive measures taken by Zionists following Thursday's disappearance of the three Zionist youngsters.
Home to roughly 1.8 million people, the coastal enclave has six border crossings controlled by Zionist entity and one by Egypt.
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