The draft law, which sparked outrage around the Arab and wider Muslim world, is set to be submitted to its first reading in parliament tomorrow.
Its original form was amended last week to not affect the sirens that announce the start of the Jewish day of rest at sundown each Friday.
Rivlin today hosted in his Jerusalem residence a meeting of religious leaders "seeking to bridge gaps over the issue of the muezzins," the Muslim lay officials charged with calling the faithful to prayer across the country, a statement from his office read.
Rivlin, whose post is mainly ceremonial, considers the new legislation - supported by Prime Minister Benjamin Netanyahu - unnecessary.
"The president believes that the existing legislation on noise levels is able to answer problems arising from this issue, along side dialogue between the different faith communities in Israel," Rivlin's spokesperson Naomi Toledano Kandel said.
Arab Israeli lawmaker Ahmed Tibi has vowed to appeal to the High Court of Justice if the Shabbat siren is excluded from the scope of the bill on the grounds that it discriminates between Jewish and Muslim citizens.
The law would apply to mosques in annexed Arab east Jerusalem as well as Israel, although the highly sensitive Al-Aqsa mosque compound - Islam's third holiest site - will be exempted, according to an Israeli official.
The bill's sponsor, Motti Yogev, of the far-right Jewish Home party, says the legislation is necessary to avoid daily disturbance to the lives of hundreds of thousands of non-Muslim Israelis.
On Sunday, Rivlin had told Turkish President Recep Tayyip Erdogan that Israeli legislative initiatives pertaining to prayers would be "considered with sensitivity, as any matter of freedom of speech and religion should be.
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