Ismail Haniya, deputy head of Hamas's political bureau, condemned the move.
"This decision will not pass," he said after Friday prayers in the Gaza Strip, which the Islamists run.
"Our people and nation will raise the Azan all over the world," he said, using the Arabic word for the Muslim call to prayer.
While the bills in theory would apply to any religious place of worship, Muslims say they are clearly meant to silence the traditional call to prayer at mosques.
The measures have become commonly known as the "muezzin law" after the Muslim official charged with calling the faithful to prayer, often through powerful speakers mounted on minarets.
The notion of Israeli legislation silencing mosques has sparked outrage around the Arab and wider Muslim world.
Supporters of the move say it is needed to prevent daily disturbance to the lives of hundreds of thousands Israelis.
Wednesday's bills were approved after a heated discussion that turned into shouting matches between ruling coalition members and Arab lawmakers, some of whom tore copies of the legislation and were ejected from the chamber.