The unprecedented warning was delivered to Palestinian President Mahmoud Abbas in a letter as Israel debated a deal offered by Hamas to free Corporal Gilad Shalit.
It came as Israeli military officials readied a second invasion force for a huge offensive into Gaza.
Hamas's Gaza-based political leaders, including Mr Haniyeh, had already gone into hiding.
But last night's direct threat to kill Mr Haniyeh, a democratically elected head of state, sharply raised the stakes.
The bid to free Corporal Shalit was brokered by Egyptian President Hosni Mubarak, who last night warned Hamas it faced severe consequences if it did not curb its "extreme stance" and described the growing conflict as a lightning rod for Palestinian vengeance.
Jerusalem has made no official comment, but Egyptian state media said Israel had found the offer unacceptable. Israel has not spelt out the terms demanded by Hamas, but earlier this week it refused to buy into talk of a prisoner swap.
I think it's safe to say that Israel is getting weary of playing footsie with these vermin. I can't say I blame them.
Next up: The Bush Adminstration will chide Israel for being too "extreme" and the American Left will turn up the volume on their wailing about the poor, put-upon Palestinians.
What was that about a world-wide war on terror?