Foreign Minister Avigdor Lieberman's party wants to ban Israeli Arabs from marking the anniversary of what they term "the Catastrophe" or Nakba, when in 1948 some 700,000 Arabs lost their homes in the war that led to the establishment of the state of Israel.
The ultranationalist Yisrael Beitenu party said it would propose legislation next week for a ban on the practice and a jail term of up to three years for violators.
"The draft law is intended to strengthen unity in the state of Israel and to ban marking Independence Day as a day of mourning," said party spokesman Tal Nahum.
The initiative could fuel racial tensions stoked by Lieberman's February election campaign call to make voting or the holding of public office in Israel contingent on pledging loyalty to the Jewish state.
Arabs, who make up 20 percent of Israel's population, said the allegiance demand was aimed at them and accused Lieberman of racism.
Israel celebrated its Independence Day this year on April 29, in accordance with the Hebrew lunar calendar. Palestinian refugees around the world and Israel's Arab citizens mark the Nakba on May 15, the day after the British mandate over Palestine ended in 1948.
Ceremonies in the West Bank were held a day early this year because May 15 falls on Friday, the Muslim day of rest.
In Ramallah, hundreds of Palestinians, some holding large wooden keys to symbolize the keys of homes from which they fled in 1948, took part in a rally.
"I came here to show that we believe that one day we will return. If not me, then my son," said Mohammad Hassan, 79.
Palestinian President Mahmoud Abbas, on a visit to Syria, was to make a televised address later in the day to mark the Nakba.
The right-leaning government of Prime Minister Benjamin Netanyahu, in which Lieberman's party is a key ally, has not endorsed the Western and Arab-backed goal of Palestinian statehood.
It also firmly opposes the division of Jerusalem and the right of return of Palestinian refugees, and Netanyahu recently introduced a demand that Palestinians, as part of any future peace agreement, recognize Israel as a "Jewish state".
Want to enjoy 'Zen' reading - with no ads and just the article? Subscribe todaySubscribe now