Oren Hazan, a provocative figure from Prime Minister Benjamin Netanyahu's Likud party, dispensed the abuse on Monday after boarding a bus of Palestinians allowed to exit the Gaza Strip to see family members held in an Israeli jail.
"Your relatives belong in the ground," he says in the footage, demanding that passengers denounce "terrorist acts" against Israel.
"Your son is a dog," he tells a woman from the coastal enclave.
One woman replies: "Speak to Hamas to see your children, not us."
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Footage of the incident has been shared widely on Palestinian and Israeli social media, and prompted a rare response from a spokesman for the armed wing of Hamas.
"Instead of sending an idiot to carry out childish acts... try to resolve the issue with courage and without intimidating women," Abu Obeida said in a statement to the Israeli authorities.
In 2015, he was suspended from his position as deputy speaker of Israel's parliament after a televised report accused him of involvement in pimping and drugs.
This May, Hazan was heavily criticised after taking a selfie with US President Donald Trump as he landed in Israel.
In August, Netanyahu intervened to stop Hazan meeting a Jordanian lawmaker on the border, fearing a fistfight.
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