Four people were reported to have been shot dead today when the Israeli military opened fire on a group of Syrians trying to cross the border along the Israeli-controlled Golan Heights.
Israeli military officials said only that troops fired warning shots at the infiltrators. But Channel 2 TV said four people were killed in the incident.
Israel's national rescue service said 10 to 20 people were wounded and are being treated in Majdal Shams, an Arab Druse town in the Golan.
Israel captured the Golan from Syria in the 1967 Mideast war. Although Syria demands the area back as part of any peace deal, the border has been quiet for decades.
The shootings occurred as Palestinians were marking the mass uprooting that occurred 63 years ago at the time of Israel's establishment. It was unclear whether the infiltrators were Palestinians.
Earlier Israel fired two tank shells and several rounds from machine guns as Gazans approached the heavily fortified border with Israel, wounding at least 15 youths.
The march near the Gaza-Israel border was part of Palestinian commemorations of their uprooting.
Across the West Bank and Gaza, thousands took to the streets, waving flags and holding old keys to symbolise their dreams of reclaiming property they lost when Israel was created on May 15, 1948.
In Gaza, dozens of marchers approached the border with Israel, and Israeli troops opened fire. The tank shells fell in an empty field several hundred yards from the group.
Palestinian health official Adham Abu Salmiya said 15 people were wounded by bullets and shrapnel. All of them were under 18 years old, and one was in a critical condition, he said.
In a West Bank refugee camp and on the outskirts of Jerusalem, soldiers fired tear gas to break up large crowds of stone throwers. But there were no signs of the mass unrest Israel had prepared for by deploying thousands of troops and sealing the West Bank.
The commemorations mark what the Palestinians call the "nakba", or "catastrophe". In the fighting over Israel's creation, hundreds of thousands of Palestinians fled their homes or were driven out.
The dispute over the fate of the refugees and their descendants, now numbering several million people, remains a key issue in the Mideast conflict.
Leaders of the two Palestinian political camps - Gaza's Islamic militant Hamas rulers and the internationally backed government in the West Bank - sent sharply contrasting messages today.
In the West Bank, Prime Minister Salam Fayyad said Palestinians hope this will be the year "in which our people achieve freedom and independence".
Fayyad, engaged in building a Palestinian state from the ground up, said it should arise in the West Bank, Gaza and east Jerusalem, the territories Israel captured in the 1967 Mideast war.
In Gaza, Fayyad's Hamas counterpart, Ismail Haniyeh, told thousands of Muslim worshippers during a dawn sermon that Palestinians mark the occasion "with great hope of bringing to an end the Zionist project in Palestine".