The bill, which defines Israel as the "national home of the Jewish people", passed its first vote in the Israeli parliament on Wednesday, after it received unanimous backing from a government committee on Sunday.
Prime Minister Benjamin Netanyahu has vowed to get the measure on to the statute books within 60 days.
Among its provisions, the legislation - popularly known as the Jewish Nation-State Bill - revokes the status of Arabic as an official language, even though it is the mother tongue of one in five citizens.
Israel's population includes a large minority of 1.7 million Palestinians.
The legislation affirms that world Jewry has a "unique" right to national self-determination in Israel, and calls for the government to further strengthen ties to Jewish communities outside Israel.
It also increases the powers of so-called "admissions committees" that block Palestinian citizens from living in hundreds of communities that control most of Israel's land.
In addition, critics are concerned that the legislation is intended to stymie any prospects of reviving peace talks with the Palestinian leadership in the Occupied Territories. US President Donald Trump is due in the region later this month in what is widely assumed to be an attempt to kick-start a long-stalled peace process. 
Netanyahu, however, has already indicated that he will insist on a precondition that Mahmoud Abbas, president of Palestine, recognise Israel as a Jewish state. The new bill effectively sets out the terms of the state Abbas is expected to recognise.
Netanyahu said this week that all Zionist parties in parliament would be expected to support the legislation. "The bill establishes the fact that the State of Israel is the nation-state of the Jewish people in our historic homeland," he told supporters of his Likud party.
He added: "There is no contradiction at all between this bill and equal rights for all citizens of Israel."