Israel Prime Minister Benjamin Netanyahu says, "We will keep ensuring civil rights in Israel's democracy, these (rights) will not be harmed, but the majority also has rights and the majority decides".
The bill, backed by the right-wing government, passed through parliament after months of political argument and some Arab lawmakers shouted and ripped up their papers after the vote.
The ministry also condemned the law - describing the right to self-determination in Israel as only belonging to Jewish people - as "antiquated" and "discriminatory". One clause downgrades the Arabic language from official to "special" standing.
In a similar stance, top Palestinian Authority negotiator, Saeb Erekat, took to Twitter on Thursday to censure the law, which he said "officially legalizes apartheid and legally defines Israel as an apartheid system".
The pan-Arab body warned that the bill will ignite discrimination and more attacks against Palestinians within the green line.
"While the democratic State of Israel facilitates freedom of religion and affords people of various backgrounds the right to visit and reside there, the reality is that Israel is inherently a Jewish state and affirming that fact does not contravene the liberties that it benevolently bestows to individuals of other faiths", it continued.
Ever since its inception in 1947, Israel was always seen as a Jewish homeland.
Another controversial segment of the law says that the State views "the development of Jewish settlements as a national value and will act to encourage and promote its establishment".
Fears over the high birth-rate of Israeli Arabs, as well as possible alternatives to a two-state solution to the Israeli-Palestinian conflict which could challenge Israel's Jewish majority, have spurred on calls to anchor the Jewishness of Israel in law.
But opponents to the law say it marginalises the country's Arab minority.
Israel, which was boosted by the decision of the USA and some other countries to shift their embassies to Jerusalem, on Thursday (July 19) passed a strong law saying only the Jews have their right of self-determination in the country, sparking a new controversy in the region.
"Israel has a long and commendable record of respect for and protection of the rights of all its citizens including its ethnic and religious minorities, but provisions in the law could impact these protections", he added. For example, the left-wing Meretz party put forward an amendment to change the bill's name from "Israel - the nation-state of the Jewish People" to "Israel - For Orthodox Jews Only". Adalah, an Arab rights NGO, said the law was an attempt to advance "ethnic superiority by promoting racist policies". Hundreds of thousands were forced to leave their homes or fled.