Hours after the demolition notice was handed over, the father appeared in a video that then circulated widely in Palestinian media.
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In Ashkelon, an Israeli city less than 10 miles from Gaza, two people were killed in rocket attacks Tuesday, Israel's Zaka emergency response team said.
The violence came as some Israelis were celebrating the anniversary of their country's capture of the Old City and its eastern neighborhoods in the 1967 Six-Day War.
Reuters reported that it was hit by an Israeli airstrike, and the Israeli military confirmed Tuesday that it struck a multistory building in Gaza's Rimal neighborhood that it said was being used by Hamas.
Israeli security forces have stepped up operations in recent weeks in the West Bank -- particularly around Jenin, where there are active fighters from several Palestinian armed groups.