Orange's statement came just hours after its chief executive was accused of giving in to a pro-Palestinian campaign.
Orange, which is partly controlled by the French government, insisted its decision to end its brand-licensing agreement with Partner, Israel's second largest mobile operator, was not politically motivated.
But Israel lashed out at the decision, which appeared to be related to Partner's operations in the occupied West Bank.
Citing its own "brand development strategy", Orange said it did not wish to maintain a brand presence in countries "in which is it not an operator", while distancing itself from the politics.
But in Friday the firm's chief insisted it had nothing to do with politics, claiming the company "loved Israel".
The company's chairman and chief executive Stephane Richard said an international campaign to boycott Israel in response to its decades-old occupation of the Palestinian territories had played no part in the decision.
"This has nothing to do with Israel, we love Israel, we are in Israel, in the enterprise market, we invest money in innovation in Israel, we are a friend of Israel, " Richard told Israel's Yediot Aharonot newspaper.
French Foreign Minister Laurent Fabius weighed into the row on Friday saying Paris was "firmly opposed" to any boycott of Israel.
"Although it is for the president of the Orange group to determine the commercial strategy of the company, France is firmly opposed to a boycott of Israel," Fabius said in a statement.
The storm erupted on Wednesday when Orange chief executive Stephane Richard told reporters in Cairo that the company was planning to withdraw from Israel.
His remarks touched a raw nerve in Israel which is growing increasingly concerned about global boycott efforts and the impact on its image abroad.
"I call on the French government to publicly renounce the miserable remarks and the miserable action of a company that is under its partial ownership," Netanyahu said after Orange's announcement on Thursday.
"I call on our friends to unconditionally declare -- in a loud and clear voice -- that they oppose any kind of boycott of the state of the Jews," he added.
President Reuven Rivlin said that "boycott" and "delegitimation" efforts against Israel existed even before the state's creation and the motivation was "no different" from today.
Isaac Benbenisti, who becomes chairman of Partner on July 1, said he was "very, very angry", accusing Richard of caving in to "very significant pressure" from pro-Palestinian activists and joining a global campaign to isolate Israel.
End of the affair
Richard's remarks dominated the headlines in all of Israel's main media outlets Thursday where he was immediately cast as a supporter of the boycott movement.
Although the Orange boss did not directly refer to Jewish settlements, his remarks in Cairo came after the publication on May 6 of a report accusing the telecoms giant of indirectly supporting settlement activity through its relationship with Partner.
Compiled by five mainly French NGOs and two trade unions, the report accuses Partner of building on confiscated Palestinian land, and urges Orange to cut business ties and publicly declare its desire to avoid contributing to the economic viability of the settlements.
The international community regards all Israeli construction on Palestinian land seized during the 1967 Six-Day War as illegal.
Challenged in Cairo, Richard said: "Our intention is to withdraw from Israel. It will take time" but "for sure we will do it".
"I am ready to do this tomorrow morning... but without exposing Orange to huge risks."
Orange says it holds no shares or voting rights in Partner Communications, nor does it have any influence over the firm's strategy and it has no other business activity in Israel.
Orange and Partner are linked by a licensing agreement which allows the Israeli firm to use its brand and logo in exchange for a fee.
The contract was signed in 1998, two years before the telecoms giant was acquired by France Telecom.
The contract, initially open-ended, was recently amended by Orange and now expires in 2025.
Orange is present in 20 countries and the brand licensing agreement with Partner is the only one with a firm that is not a subsidiary.