Police were on Monday searching the Golan for infiltrators from Syria who broke in during a day of bloodshed which saw 12 killed as thousands marched on Israel's borders.
Around 300 protesters were also injured on Sunday as Israeli troops fired on thousands of people along the Syrian and Lebanese borders, as well as in the Gaza Strip and the West Bank.
The protests came as Palestinians in the territories and in the neighboring countries staged massive protests to mark the anniversary of Israel's founding in 1948, in an event known in Arabic as the "nakba" or "catastrophe."
Israeli police spokesman Micky Rosenfeld said hundreds of police had been working through the night in the Golan Heights town of Majdal Shams to seek out any protesters who had not returned to Syria.
"Throughout the night, police have been searching house-to-house for suspects who could still be in Majdal Shams," he told AFP, saying police had set up roadblocks throughout this Druze town, which has a population of 9,700 and lies close to the Syrian border.
He said police had stopped a taxi heading out of the town with a 34-year-old Syrian passenger, who was being questioned by police along with the driver, a Palestinian from east Jerusalem.
The border breach in the Israeli-occupied Golan Heights was one of the worst incidents of violence there since a 1974 truce accord, while the bloodshed along the Lebanese border was the bloodiest confrontation since the 2006 war between the two neighbors.
Syria lashed out at Israel, warning it would bear full responsibility for its "criminal" actions, while Lebanon filed a complaint to the United Nations, urging it "to make the Jewish state halt its aggression and provocation," the official NNA news agency reported.
UN Secretary General Ban Ki-moon expressed deep concern over the violence and urged all sides to show the "utmost responsibility" to ward off new hostilities, a UN spokesman said.
But Israeli Prime Minister Benjamin Netanyahu said the Jewish state was "determined" to defend its borders against protestors bent on denying Israel's right to exist.
"Their struggle is not over the 1967 borders, but it questions the very existence of Israel, which they describe as a catastrophe which must be resolved," he said on Sunday.
In the Golan Heights, at least two people were shot dead, a local Druze doctor told AFP, while paramedics confirmed the same toll, saying one had been shot in the head, and the second in the chest. They also treated another 20 people for light to moderate injuries.
Along the Lebanese border, Israeli gunfire killed 10 people and wounded 110 as thousands of mainly Palestinian refugees demonstrated along the tense frontier, medical sources said.
And along Gaza's northern border with Israel, 125 people were injured, five of them seriously, when troops opened fired as more than 1,000 Palestinians marched on the Erez crossing.
At least half of the wounded were minors, medics said.
Elsewhere, at least 29 others were injured in clashes across annexed east Jerusalem and in the West Bank.
The army said "hundreds of Syrian rioters" had crossed onto the Israeli side, and troops had "fired selectively" towards them, while along the Lebanese border, soldiers had opened fire to warn off protesters trying to breach the fence. Thirteen soldiers were also injured in the two incidents, it said.
Since Friday, Palestinians and Arab Israelis staged a series of events in the run-up to Sunday's anniversary.
Meanwhile, a 22-year-old Arab Israeli truck driver was due in court after he ploughed into 12 cars and a bus in Tel Aviv on Sunday, killing one, in what police believe was a deliberate attack.
"He shouted 'Allahu Akbar' at the scene," said Rosenfeld. "He struck 12 cars then he hit a bus and his truck stopped. He got out of the truck and started attacking people," he said, saying bystanders had wrestled him to the ground.
More than 760,000 Palestinians -- estimated today to number 4.8 million with their descendants -- were pushed into exile or driven out of their homes in the conflict that accompanied the Jewish state's foundation.