Hundreds of police fanned out across the Golan Heights on Monday in search of refugees who crossed over from Syria in some of the bloodiest violence in years along Israel's borders.

In Lebanon, Syria and the Palestinian territories, people gathered to mourn the 14 people killed when Israeli troops opened fire on thousands of protesters who sought to breach its northern borders.

Hundreds were injured in the occupied Golan Heights, as well as in clashes with Israeli troops in the West Bank and northern Gaza Strip as Palestinians marked the anniversary of Israel's founding in 1948, in an event known in Arabic as the "nakba" or "catastrophe."

Israeli police spokesman Mickey Rosenfeld said house-to-house searches were ongoing on Monday afternoon and roadblocks had been set up around the Golan Heights town of Majdal Shams, where protesters who crossed over from Syria gathered.

On Monday morning, police detained a a 34-year-old Syrian, who was trying to leave the town in a taxi driven by a Palestinian from east Jerusalem, he said.

Brigadier General Yoav Mordechai told army radio the military remained "in a state of high alert in the north, the south and the centre."

Defence chiefs also extended a 24-hour lockdown on the occupied Palestinian territories which had been due to end at midnight on Sunday.

Sunday's violence was some of the worst in the Israeli-occupied Golan Heights since a 1974 truce accord, and the clashes along the Lebanese border marked the bloodiest confrontation since the 2006 war between the two neighbours.

Most of the victims were in Lebanon, where 10 people were killed and 110 injured when Israeli troops opened fire on people trying to scale the border fence.

Another four people were killed when they entered the Golan Heights, along with hundreds of other protesters, Syrian medics said.

The Israeli army said "dozens" had been injured in the two incidents, along with 13 soldiers.

In Gaza, 125 people were injured, five of them seriously, when troops opened fired as more than 1,000 Palestinians marched on the northern Erez crossing.

Elsewhere, 29 others were injured in clashes in the West Bank and annexed east Jerusalem.

Palestinian refugee camps across Lebanon declared a day of mourning, with shops observing a general strike ahead of the funerals for the 10 victims, which were taking place in four refugee camps on Monday.

In the Palestinian territories, President Mahmud Abbas announced a two-hour strike in all public institutions except schools and ordered all Palestinian flags be flown at half-mast.

Hassan Nasrallah, head of the Lebanese Shiite militia group Hezbollah praised the protesters, saying they had "given the nakba new meaning," and Hamas chief Khaled Meshaal, speaking from Damascus, condemned Israel's "new Zionist crime against our people who were demonstrating peacefully."

Lebanon has filed a complaint with the United Nations, urging it to make Israel "halt its aggression and provocation" while Syria warned that the Jewish state would bear full responsibility for its "criminal" actions.

Israel responded by saying it would file its own complaint against both Syria and Lebanon, accusing them of violating Israeli borders.

UN Secretary General Ban Ki-moon expressed deep concern over the violence and urged all sides to show the "utmost responsibility" to avoid new hostilities, a spokesman said.

Filippo Grandi, head of the UN agency for Palestinian refugees, also condemned the bloodshed, saying it proved the need for a solution to the plight of the refugees, who now number 4.8 million.

But Israeli Prime Minister Benjamin Netanyahu said the Jewish state was "determined" to defend its borders against protesters bent on denying Israel's right to exist.

On Monday morning, an Israeli court extended the detention of a 22-year-old Arab Israeli truck driver accused of ploughing into 12 cars and a bus on Sunday, killing one, in what police believe was a deliberate attack.

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.