Palestinian Energy and Natural Resources Authority in Gaza said electricity was reduced by 8 megawatts to the 2 million residents.
Last week, Israel approved a requested by the Palestinian Authority to cut the electricity it supplies by 42 megawatts. Normally, Israel provides 120 megawatts via 10 electrical lines for about four hours of electricity.
The area would see 2 to 3 hours of electricity daily once Israel end its reductions, said Gaza electricity distribution company spokesperson Mohammad Thabbet to the Gaza-based news site al-Raiy.
Gaza's only power plants stopped operating in August so residents and businesses rely on electricity from Israel as well as batteries, generators and candles.
Muhammed Thabet, the Gaza Electricity Distribution Company spokesman, told The Jerusalem Post that the 8 megawatt reduction is "unjust and dangerous."
"There is incredible demand for electricity during Ramadan. People stay awake all night and shops remain open," Thabet said. "The electrical networks in Gaza are under immense pressure."
Hamas spokesman Sami Abu Zuhri said in a statement that "the occupation bears full responsibility for the consequences of the electricity reduction because it collect taxes along Gaza's crossings that are enough to pay for Gaza's electricity and other [expenses]."
Hamas seized control of Gaza from Abbas' Fatah party in 2007.
The Israeli Defense Ministry branch is responsible for overseeing the transfer of electricity to Gaza.
On Thursday, Defense Minister Avigdor Liberman said that Israel was strictly the "supplier of electricity and was prepared to supply electricity" if the Palestinians paid for it. "This is an [internal] Palestinian crisis; those who need to pay for electricity are the leaders of Hamas, of the Palestinian Authority -- we are not a party in this," he said.
Last Wednesday, U.N. Humanitarian Coordinator Robert Piper said "a further increase in the length of blackouts is likely to lead to a total collapse of basic services, including critical functions in the health, water and sanitation sectors."