Reconciliation attempts since then between rival governments in the West Bank and Gaza have failed. Palestinian officials in the West Bank had no immediate comment.
Hamas has said it would not be cowed.
Hamas official Ismail Radwan condemned the move by Abbas. "It's illogical that Gaza is besieged and deprived of electricity, water and basic needs for the sake of political prices," he said.
Gaza has suffered through increasing hardship since the Hamas takeover, which triggered a border blockade by Israel and Egypt. Gazans have endured power cuts, with electricity now available for only six hours a day.
COGAT, a branch of the Israeli military, says it was notified by the Abbas government that electricity payments will stop immediately.
The renewed push to regain a foothold in Gaza comes ahead of Abbas' meeting with President Donald Trump at the White House next week. Abbas is under pressure to show that he represents all Palestinians, including those in Gaza.
Khalil al-Haya, the second highest ranking Hamas leader in Gaza, told The Associated Press on Wednesday that Abbas will fail "if he tries to make Gaza kneel or expects to win our loyalty by force."
He said: "Gaza is an explosive barrel and he cannot press this barrel more. If he does, it's going to explode in his face and in all directions.
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