Palestinians accuse Israeli settlers of setting mosque on fire and spraying graffiti on wall in Hebrew.
A Palestinian fighter has been killed as Israeli air raids on Gaza enter their third day, bringing the death toll to nine.
The latest attack took place on Wednesday in the southern town of Rafah. The victim is believed to be a member of Islamic Jihad.
The fighter died and a comrade was wounded in the attack on their motorcycle in the city located near Gaza’s frontier with the Egyptian Sinai, medical officials said.
Israel said the man targeted had been involved in a raid on Monday from adjacent Sinai territory into Israel, which killed an Israeli.
Israeli fighter jets also carried out three raids against the Gaza Strip early on Wednesday, Palestinian security officials said.
The raids targeted a training centre for the Ezzedine al-Qassam Brigades, the armed wing of Hamas at Rafah in the south of the Strip, a “workshop” in Gaza City, and Hamas naval police installations in the north.
Israeli guards wounded
A spokesman for the Brigades said his organisation had fired 45 rockets in 24 hours at Israeli territory, a figure confirmed by Israeli police who said four border guards had been wounded, one seriously.
Hamas, which rules Gaza and has observed an unofficial truce with Israel, launched on Tuesday rocket attacks for the first time in more than a year.
In a rare show of force, fighters from the Brigades said they would continue firing unless the air raids ended.
“This is our answer to the Zionist crimes. It will continue if they carry out more strikes on Gaza,” the group said in what was an unusual departure from their customary observance of a tacit truce with Israel.
Wednesday’s death raises to eight the number of Palestinians killed in the series of deadly Israeli raids which began on Monday morning, just hours after armed men from Sinai carried out an ambush along Israel’s southern border with Egypt, killing an Israeli civilian.
Israel has said the sudden spike in air raids was “in no way related” to the border incident, with the military saying the air force was targeting fighters about to attack.
A Gaza Palestinian official who requested anonymity told AFP news agency that Egypt was making efforts to restore calm between the Palestinian movements and Israel.
The official said the Palestinian movements were “ready for a return to calm as long as Israel ends its attacks”.
Egypt has brokered Gaza truces in the past and an Egyptian official said renewed mediation had secured agreement by Israel and Palestinian factions on Tuesday night.
A Palestinian source accused the Israelis of violating the deal.
Israel neither confirmed nor denied there was such deal, and the military said in a statement it would “continue to operate with perseverance and determination against those who use terror against the State of Israel”.
The last major flare-up in Gaza was in March when four days of tit-for-tat violence left 26 Palestinians dead, and saw armed groups firing more than 200 rockets into Israel.