At the end of May, five non-governmental organisations and two unions in France asked Orange to state publicly its willingness to sever its ties with Partner and denounce "attacks on human rights" they said the Israeli company had carried out.
They say Partner Communications Co has a licence from Orange to use its brand.
The report claims that Partner, operating in Jewish settlements in the occupied West Bank, was contributing to their economic viability and to perpetuating a situation considered illegal by the international community.
When asked about this on Wednesday, Orange's Stephane Richard said in Cairo that "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."
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Orange has previously said it inherited the contract with Partner, in which it holds no shares or voting rights, and that it has no influence over the Israeli firm's management and strategies.
Richard was speaking at a news conference held in connection with a visit to Orange's nearly wholly owned Mobinil unit in Egypt.
In Israel, deputy foreign minister Tzipi Hotovely wrote to Richard asking for clarification.
"I must admit to have been taken aback by these reports which do not become a responsible global company such as Orange," she said in the English-language letter, a copy of which was seen by AFP.
"I am confident that these reports do not reflect the intent of your company. I therefore urge you to clarify the matter as soon as possible."
Partner's website showed no immediate reaction to Richard's comments, but business daily Globes quoted Partner CEO Haim Romano as saying that he "regretted what was said".