Dozens of people were injured when Israeli troops opened fire as a group of demonstrators from Syria tried to break through a border fence at the Israeli-occupied Golan Heights.
Forty-five people were injured in the incident.
Across the West Bank and Gaza, hundreds took to the streets in demonstrations marking the anniversary of Israel's creation in 1948.
In northern Gaza, at least six people were injured when Israeli soldiers opened fire on a group of young demonstrators approaching the border.
Outside Jerusalem, soldiers fired tear gas and rubber bullets to break up a group of people throwing stones.
Israel had heightened security in anticipation of unrest leading up to Sunday's protests marking "Naqba" - or "the catastrophe." Some activists have called for a new "intifada" - or uprising - against Israel.
Earlier Sunday, Israeli police say one person was killed and several injured when a truck ran into several vehicles in Tel Aviv.
Officials say the truck struck a bus and several cars in what they say may have been a planned attack. At least least two people were seriously injured.
The driver, described as an Arab Israeli, was arrested and is being questioned by police.
More than 700,000 Palestinians are estimated to have fled or been forced to leave their homes during the war that followed Israel's declaration of statehood in 1948.
Israel, which uses the Hebrew calendar, celebrated its 63rd anniversary on Tuesday.