Adds details; Netanyahu, Abbas comments (first version posted at 18:20)
Palestinian commemorations on Nakba (catastrophe) day - the anniversary of Israel's founding - turned violent Sunday, as hundreds of protestors tried to storm the borders with Israel, and rioting took place north of Jerusalem, dpa reported.
By late afternoon, at least 18 protestors had been killed in separate incidents along Israel's border with Lebanon, and along the border between Syria and the Israeli-occupied Golan Heights.
Scores of Palestinians were injured along the borders, in the Gaza Strip in the south, and during demonstrations north of Jerusalem.
Palestinian President Mahmoud Abbas said the blood of those killed fighting for their rights "will not go to waste."
"Their blood was spilled for the freedom of our Palestinian people and for its rights," he said in a televised statement.
The large numbers involved showed that "right is stronger than time, and the will of people is stronger than the power of the oppressive forces and the occupiers."
Israeli Prime Minister Benjamin Netanyahu said Israel was "determined to defend our borders and our sovereignty."
In a brief televised statement, he said the protestors were motivated by a desire to undermine Israel's legitimacy and right to exist.
The Golan Heights saw the most dramatic incident where, in an unprecedented act of defiance, Palestinians forced their way across the border, prompting the Israeli army to open fire.
Syrian reports said eight protestors were shot dead, but Israel Army Radio reported that Israel returned 10 bodies to the Syrians.
Apart from isolated incidents, it was the first time the heavily- secured border had been breached since 1973, when Syrian tanks took Israeli forces by surprise in the Yom Kippur War.
An Israeli military statement said the Israel Defence Forces (IDF) "opened fire in order to prevent the violent rioters from illegally infiltrating Israeli territory." Three Israelis were also injured.
One witness said thousands breached the normally heavily-guarded border. He said they were walking through a minefield, waving Palestinian and Syrian flags.
By early evening, the protestors had returned to Syria, or were in the process of doing so.
An Israeli military statement accused the Syrians of complicity in the breach of the border fence.
"The Syrian regime is intentionally attempting to divert international attention from the brutal crackdown of their own civilians," said an Israeli military statement.
Elsewhere along Israel's northern border, 10 people were killed and 70 others wounded in a Nakba day incident in southern Lebanon as Palestinian protesters tried to push their way across the border with Israel, local media reports said.
The demonstrators were shot at by Israeli troops when they defied calls by the Lebanese army and organizers of the so called "peaceful rally" not to approach the fence separating Israel from Lebanon.
Carrying Palestinian flags and chanting "we want our land back" thousands of Palestinians tried to approach the electric fence that separates Lebanon from Israel, but Lebanese army troops fired in the air and ordered the crowd to return to where the rally was held.
The demonstrators pelted the Lebanese army with stones as it struggled to hold them back from the security fence.
Around 50 protesters reached the fence and started throwing stones at Israeli soldiers on the other side, prompting the Israeli soldiers to fire their guns and tear gas at the protesters.
The protesters headed by buses to Maroun al Ras, a Lebanese village few kilometres away from the Israeli border, where a huge rally was held.
Further south, in the Gaza Strip, one Palestinian was killed, and at least 82 injured.
Palestinians in the Strip tried to march to the Erez crossing point, at the northern end of the salient, but were deterred by Israeli shells and small arms fire.
In the West Bank, hundreds of Palestinians hurled rocks at Israeli troops at the Kalandia checkpoint near Ramallah.
At least 19 people were injured in Jordan as police dispersed hundreds of activists who tried to reach the Israeli-controlled border with the West Bank, the official Petra news agency reported.
The agency said 11 activists and 8 policemen were hurt as the security authorities intervened to end clashes between participants in a rally staged by a group calling itself the May 15 Youth and citizens living in the Karameh area, a few hundred metres from the border.
Meanwhile, one person was killed and 17 wounded, in Tel Aviv when a truck went out of control, hitting a bus and several cars.
The Arab-Israeli driver said he had lost control of the vehicle after a tyre burst, but police said they suspected an intentional attack coinciding with Nakba Day.
Nakba day commemorates the dispersal of some 800,000 Palestinians to refugee camps in the region in the Arab-Israeli war of 1948.
The number of Palestinians living in refugee camps outside Israel - in Jordan, Lebanon, Syria, Gaza and the West Bank - is currently some 4.8 million.