Nakba Day, as Palestinians call it, is an important date in the political calendar
Israeli campaigners and left-wing lawmakers have condemned moves to ban Israeli Arabs from marking the Nakba - the Palestinian "catastrophe" of 1948.
On Sunday an Israeli government panel backed putting the bill, proposed by the party of far-right Foreign Minister Avigdor Lieberman, before parliament.
A Labour minister opposed it; Hadash, a mainly Arab party, called it "racist".
Some 700,000 Palestinians fled or were forced from their homes in 1948-49 as Israel claimed its independence.
About 20% of Israel's population are descended from Arab citizens of British Mandate Palestine who remained on the territory that became Israel.
Along with Palestinians in the West Bank, Gaza and around the world, Israeli Arabs
mark the yearly Nakba
anniversary on 15 May with mourning and commemoration events.
celebrate their Independence Day,
marking the creation of their state, at the same time of year, although according to the Hebrew calendar.
Under the proposed legislation, people caught marking the Nakba could be jailed for up to three years.
Avigdor Lieberman's party, Yisrael Beiteinu, says the bill is "intended to strengthen unity in the state of Israel".
The Hadash MK Hanna Swaid called it "racist and immoral" and "a fierce insult on democratic and political rights".
Social Affairs Minister Isaac Herzog, said it "could impair freedom of expression and freedom of protest and achieve the opposite goal - increasing alienation and strengthening extremists".
He is a member of the Labour party, which is part of the right-leaning governing coalition, together with Yisrael Beiteinu party and led by Prime Minister Benjamin Netanyahu's Likud party.
Correspondents say that although there have been unsuccessful attempts to introduce similar bills in the past, the right-wing make-up of the current government gives this one more chance of passing - although it has many hurdles to clear yet.
An Israeli rights organisation, the Association for Civil Rights in Israel, (Acri) said the committee's initial approval of the bill was "a sign of a democracy losing its bearings".
"Marking the Nakba does not threaten the safety of the State of Israel, but is rather a legitimate and fundamental human right of any person, group or people, expressing grief at the face of a disaster they experienced," said Acri president Sammi Michael.
Mr Lieberman's party also wants to introduce a loyalty pledge, which would demand that Israeli-Arabs swear allegiance to Israel as a "Jewish, Zionist and democratic" state, before they can be issued with their ID papers.
Israel Beiteinu spokesman Tal Nahum said the measure would be discussed by the cabinet on Sunday and the first parliamentary vote would be the following Wednesday.
raised concerns during Israeli military operations in Gaza in January and December that some Israeli-Arabs were openly expressing sympathy with Hamas - which controls Gaza and which launches militant attacks on Israel and which, in its charter, is sworn to the state's destruction.