The Palestine Liberation Organisation's executive committee expressed in a statement its "strong condemnation and rejection of this law".
"The law aims to kill the two-state solution by imposing the project of a 'greater Israel' as well as the Jewishness of the state upon the historical land of Palestine," said the PLO, which dominates the Palestinian Authority.
Israel's cabinet on Sunday endorsed a proposal to anchor in law the country's status as "the national state of the Jewish people," voting 14 to six in favour of the initiative.
Critics, who include the government's top legal adviser, say the proposed change could institutionalise discrimination against its 1.7 million Arab citizens, descendants of the 160,000 Palestinians who stayed after Israel was established in 1948.
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And the PLO said the law was "an attempt to tarnish and twist the Palestinian historical narrative and wipe out Palestinian existence" in the region, by reserving it exclusively for Jews.
Peace talks between Israel and the Palestinians have failed time after time as the Jewish state builds more settler homes on land the Palestinians want for their future state.
But Israel's identity is already contained in its 1948 declaration of independence, according to the Israel Democracy Institute, which said that the new proposal fails to emphasise "commitment to the equality of all its citizens".