Mr Mazuz insists that his main motivation is helping small businesses which are closed on Shabbat compete with large shopping centres and retail chains, however, the law's opponents accuse him of pandering to strictly Orthodox party members.
Kulanu, the centrist party which is a member of the coalition, is opposed to the law and succeeded in removing it from the agenda of the cabinet's legislative committee on Sunday. It is now scheduled to be voted on in two weeks.
The religious parties in the coalition are expected to support the law and Likud's position is still unclear.
Kulanu MK Rachel Azaria, leading opposition to the proposal, said: "Before changes are made, we need to define what an Israeli Shabbat means today and it can't only be an Orthodox definition."
One proposal suggested by opposition parties is a period of dialogue followed by a new law which sets guidelines for which businesses will be allowed to remain open on Shabbat, mainly places of entertainment and restaurants and also some public transport.
