Critics say the move -- backed by the cabinet on Sunday -- will come at the expense of democracy and institutionalise discrimination against minorities, including Arabs.
"The aim of this law is to guarantee the future of the Jewish people on its land," Netanyahu told parliament, hitting back at "those who want to question the national right of the Jewish people (to live on) this land."
On Tuesday, President Rivlin, who also hails from Netanyahu's rightwing Likud party, said he did "not understand the interest of this law."
"Placing the state's Jewish character before its democratic character puts into question its principles in the declaration of independence, which stated Israel's Judaism and democracy were values of equal importance," Rivlin said during a speech in the southern port city of Eilat.
Israel's identity is already contained in its 1948 declaration of independence, according to the Israel Democracy Institute, which said the new proposal fails to emphasise "commitment to the equality of all its citizens".
Netanyahu insists the law would balance Israel's Jewish and democratic characteristics.
The country's parliament, the Knesset, is to vote on the proposal on December 3.
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Critics, who include the government's top legal adviser, fear it would institutionalise discrimination against its 1.7 million Arab citizens -- descendents of the 160,000 Palestinians who stayed after Israel was established in 1948.
The Palestinian leadership said Tuesday the law would "kill" Middle East peace prospects "by imposing the project of a 'greater Israel' as well as the Jewishness of the state upon the historical land of Palestine."
Separately, a Likud lawmaker submitted a proposed law to parliament that would automatically strip people involved in attacks on Israelis of their nationality or residency.
The homes of the attackers or their families would also be demolished and welfare rights withdrawn.
It comes days after Netanyahu vowed to seek new powers to revoke residency and welfare rights from Arabs if they or their relatives participate in unrest.
Annexed Arab east Jerusalem has been hit by months of violence, which has spread across the occupied West Bank and to Arab communities inside Israel.
Last week two Palestinians burst into a Jerusalem synagogue with meat cleavers and a gun and killed four rabbis and a policeman who came to their aid, in the city's deadliest violence in six years.
The following day, Israeli forces demolished the east Jerusalem home of a Palestinian who killed a young woman and a baby with his car last month before being shot dead by police.