The commemoration followed an announcement by Avigdor Lieberman, Israel's foreign minister, that he intends to ban Israeli Arabs from marking the anniversary of the Nakba.
Lieberman's ultranationalist Yisrael Beitenu party said it will propose legislation next week for a ban on the commemoration and jail terms of up to three years for those who violated the law.
"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 Tal Nahum, a party spokesman.
In the northern West Bank town of Ramallah, about 2,000 Palestinians held a rally, marching through the streets with black ribbons to signify mourning.
But in the Hamas-ruled Gaza Strip, officials from the Palestine Liberation Organisation (PLO) accused Hamas authorities of preventing them from holding any ceremonies.
Witnesses said police were deployed in the centre of Gaza City to disperse any demonstrators who tried to gather, AFP news agency reported.
There was no immediate comment from Hamas.
About 700,000 Palestinians fled or were driven out of their homes during the creation of the Israeli state six decades ago.
Palestinians demand the right for the 4.6 million descendants of those who fled in 1948 to return to their lands that are now inside Israel.