Lammy told parliament's foreign affairs select committee he would comply with the ICC's request to arrest Netanyahu if he entered Britain, insisting he had no choice but to ignore the order.
France was intended to serve the same role as the US in helping to enforce the ceasefire.
A statement by the French Foreign Ministry said it would continue to work closely with Prime Minister Benjamin Netanyahu.
The question is not whether Israel agrees with the decision but rather how it will deal with the consequences, which could be serious.
35,000 Israeli soldiers and intelligence personnel have had their details leaked on Telegram as part of an effort to try individual Israelis for alleged war crimes
Israel can counter the ICC’s biased arrest warrants against Netanyahu and Gallant with this action plan.
Several other European countries, including Ireland and Germany, have announced in the past that they will respect the judges' ruling.
His remarks came after the ICC issued arrest warrants on Thursday for Israeli Prime Minister Benjamin Netanyahu.
"I am assembling a team of world-class lawyers from around the globe to help defend Israeli leaders against the false charges," Dershowitz said.
The prime minister's request comes after the court refused his first appeal.
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