I wouldn’t be surprised. They already have made it illegal for US airlines to fly to Israel, probably to last until the Kerry ceasefire is imposed on Israel in the next few weeks.
According to the news reports ... four major USA airlines suspended their flights - indefinitely - BEFORE the FAA even acted.
It sounds like, to me, an “airline thing” and safety of their passengers, not to say anything about potential lawsuits.
And in fact, today, I read where one of the major airlines says that they evaluate their flights on their own, apart from the FAA, and they have decided on their on their own to not fly there.
ALSO ... Israel has ALREADY accepted several cease-fires. Israel is not the hold-up here. It’s HAMAS who has not accepted it ... :-) ...