Putting new pressure on Hamas, a top Israeli energy company, Dor Alon, said it was suspending fuel supplies for private use in Gaza, though the tap remained open for power stations.
"We should simply increase the isolation of Gaza," Israeli Infrastructure Minister Binyamin Ben-Eliezer told Army Radio.
But another official played down speculation Israel could try to further choke off Gaza, which is also supported by Egypt.
"We won't cut off electricity and water," Deputy Defense Minister Efraim Sneh told Israel Radio.
Fayyad serves as Palestinian prime minister, replacing Ismail Haniyeh of Hamas. He also holds the finance and foreign affairs portfolios.
Speaking yesterday after being sworn in Fayyad said that restoring security would be a difficult but not an impossible task.
"The first priority of our government is security and the security situation," he told reporters.
"The mission will be difficult and hard, but not impossible," he said.
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