The official also said Israel would connect water to a Palestinian city so that it can be inhabited, after a minister's objection had been overruled.
Speaking on condition of anonymity, the official said Israel would be taking approximately 60 million shekels ($15 million/13.5 million euros) "out every month now from what we're holding up, so the debt doesn't get larger."
Israel has been withholding hundreds of millions of shekels in taxes it collects and transfers monthly to the Palestinian Authority since early January, following the Palestinian move to join the International Criminal Court.
The Israeli Electric Corp has long been demanding the Palestinians pay their bills for electricity supplied to the West Bank and east Jerusalem, with the debt reaching nearly two billion shekels.
After repeat warnings, it again cut the power to two Palestinian cities in the northern West Bank for approximately an hour each time on Monday and again Wednesday.
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The official stressed that the deduction from tax revenues was not aimed at eliminating the entire debt, only of preventing it from growing any further.
"It's not taking all the money they owe; that's a separate issue," he said.
"The idea is to make sure that the Palestinians get their electricity, and that's the deal that has been made" with the electric company, he noted.
Separately, the official said Israel would connect a new uninhabited Palestinian city to water, after Water Minister Silvan Shalom refused to do so.
"On Rawabi, there's a green light to go ahead" and "connect the water," the official said, after the head of the Israeli military activities in the West Bank, General Yoav Mordechai, said he would approve Rawabi's water connection along with that to Israeli projects.
Shalom's red light had been due to the Palestinian refusal to participate in a joint Israeli-Palestinian water committee, since it was also in charge of approving water to Israeli West Bank settlements, to which the Palestinians objected.