Minorities and many Jewish Israelis alike have criticized the law, adopted last month, for recognizing Israel as a Jewish state and saying "the right to exercise national self-determination in the State of Israel is unique to the Jewish people."
The law also downgraded Arabic from an official language to having "special status."
Druze community members organized Saturday's march, held under the motto: "Equal rights for all citizens."
The Druze, numbering around 130,000 in Israel, have had special status since the 1950s, when they were drafted into the military, unlike Israel's Muslim and Christian populations.
The Druze feel especially discriminated against by Israel's new law. A third Druze officer resigned from the Israeli army earlier this week in protest, Israel's public broadcaster Kan reported.
The bill was passed by the right-wing governing coalition in a 62-55 vote on July 19.
Many Jewish Israelis, however, have criticized the law, including the country's president, Reuven Rivlin.
Israel's Palestinian and other Arab minority - 20 percent of the population - has also slammed the law, but the Druze community's concerns have garnered more sympathy from the governing coalition.
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