On Friday, Israeli troops killed two Palestinian youths in the northern Gaza Strip close to the border with Israel.
A spokeswoman for the Israeli army said troops had shot at figures trying to plant an object close to the barrier.
The Israeli military says areas near the border fence are no-go zones for Palestinians.
"Hamas is trying to draw us [Israel] into their civil war"
Zafon, Beersheva, Israel
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In the occupied West Bank, the Israeli army destroyed several cement barriers in a raid in the town of Nablus on Saturday.
The barriers were used by Palestinian fighters to prevent Israeli vehicles from driving through the streets, witnesses said.
Nihad Masri, the acting mayor of Nablus, said a few people were injuries as the cement barriers were blown up with explosives.
Mustafa Barghouthi, Palestinian information minister, said the destruction of the barriers in Nablus was "a new crime coming in the context of Israeli escalation against the Palestinian Authority and people".
An Israeli military spokeswoman said troops had found three explosives laboratories in Nablus this year, as well as explosive belts for use by suicide bombers.
Also on Saturday, four Palestinians in the Maghazi refugee camp in the Gaza Strip were arrested by Israeli troops, security sources said.
The Israeli army said that four people had been taken in for questioning for firing rockets from Gaza into Israel, but all four had been released.