Schabas resigned yesterday after Israeli side accused him of bias due to consultancy work he did for the Palestine Liberation Organisation.
More than 2,100 Palestinians, most of them civilians, 67 Israeli soldiers and six civilians in Israel were killed in the 50-day gaza conflict in July last year. The UN investigation, due to issue its report on March 23, is investigating violations by both sides.
In his letter, Schabas explained that Israel's complaint was linked to a brief legal opinion he had prepared for the PLO in October, 2012.
"The complaint about my brief consultancy, as I understand it, is not about the content, which is of a technical legal nature, but the implication that in some way I am henceforth beholden to the Palestinian Liberation Organisation," he wrote.