According to reports, USA officials said the alleged leak endangered the life of a spy planted within the IS by Israel.
"When it comes to ISIL, unlike Jordan, Israel relies on its electronic surveillance collection and its intelligence sharing-arrangement with its Arab partners", one of the anonymous sources said, using an alternative acronym for the group.
Donald Trump and Israeli Prime Minister Benjamin Netanyahu have spoken by phone, a spokesman said on Wednesday, as controversy brewed over the USA president's sharing of intelligence with Russian Federation that came from Israel.
"We need to punish the Americans, it's possible, so that we don't put Trump in a position where he is again tempted, we need to abstain from transferring information to him, or to only give him partial information so that he can't endanger any source", Yatom told The Times of Israel.
It said that Trump told Lavrov about a specific Islamic State group bomb threat.
The officials said they were not aware of any Israeli agents in the field operating in the Islamic State, and thus the likelihood that Israel supplied the information was low, they told Al-Jazeera Thursday.
Trump shared information about "terrorism and airline flight safety" in the Oval Office meeting.
A United States administration official confirmed to AFP on condition of anonymity that the original intelligence came from Israel, which was initially reported by the New York Times.
But the intelligence scandal could corrode trust among allies who shared classified information with the United States on the understanding that it will go no further.
Critics worry that Trump's discussion of the classified information with Russian officials could jeopardize valuable intelligence relationships between the USA and foreign countries. "This is our greatest ally, and we share with them heaps of super-secret information".
Neither Israel nor the U.S. publicized the call, during which the two leaders apparently only discussed Trump's upcoming visit to the Middle East.