Thousands of Palestinians and their supporters were embroiled in deadly confrontations with the Israeli army as protests erupting across the Palestinian territories, Israel and its borders with Syria, Lebanon and Jordan were met with live fire, rubber bullets, stun grenades and teargas.

At least 13 people were reported killed in a day of bloody confrontations, including 10 at the Lebanese border, at least two at the Syrian border and one in Gaza. However some sources said 10 people had been killed on the Syrian border. Police also fired teargas to disperse hundreds of protesters on the Jordanian border.

Although Israel had been braced for violent protests, the clashes on its borders were largely unexpected. Israeli politicians, already deeply alarmed about uprisings in its neighbouring Arab countries, now face heightened tensions with Syria and Lebanon.

Thousands of Palestinian refugees from Syria marched towards the village of Majdal Shams in the Golan Heights, which Israel captured from Syria in 1967.

According to the Israeli military "hundreds of Syrian rioters infiltrated the Israeli-Syrian border ... and violently rioted against [Israeli] forces". It said its troops "fired selectively towards rioters".

"The Israeli army warned [the protesters] not to cross but they didn't listen," Shefa Abu Jabal, 25, a resident of Majdal Shams, said. "When the crowd started to come over … soldiers started shooting.

"Around 200 have managed to get across. I've heard there are four people dead on this side and there are many more injured. People in the village are really scared. The Israel soldiers looked shocked. No one thought there would be trouble at this border."

Another resident, Hamad Awidat, said: "There are thousands and thousands of people on the Syrian border who are trying to cross. There has been a lot of fighting, and of course people are scared."

At Maroun al-Ras in southern Lebanon, Israeli troops opened fire after hundreds of protesters broke through Lebanese army barricades to throw rocks across the border. At least six people were killed. One man, apparently shot in the chest, was doused with water as protesters tried to revive him but shouts of "Allah Akhbar" broke out as his dead body was lifted over the crowd. One protester, his clothes soaked in blood, screamed: "Murderers, cowards, is a rock any match for a bullet?"

Hezbollah, which controls Lebanon's southern villages had given tacit support for the protest but the crowd was dispersed by Lebanese troops firing into the air. Yassir Ali, one of the protest organisers said the deaths were not unexpected. "Palestinian people are used to paying with their lives. It's a big price, but one we are prepared to pay to prove our right to return to the motherland."

Brigadier General Yoav Mordechai, an Israeli military spokesman, said soldiers fired when demonstrators began vandalising the border fence. The army was "aware" of casualties, he said.

UN peacekeepers on the Lebanese side of the border appealed for "maximum restraint" to prevent casualties.

The Israeli security forces had deployed about 10,000 troops and police along the country's borders and in the Palestinian territories. The West Bank was subject to a 24-hour closure, with only emergency access permitted.

Confrontations were reported after about 600 people marched from the West Bank's principal city, Ramallah, towards the Qalandia checkpoint into Jerusalem. There were also clashes in other areas of the West Bank.

In Gaza, at least 80 people were injured after Israeli troops opened fire on demonstrators approaching the Erez border crossing, Palestinian medical sources said. The Israeli military said it shot dead a man trying to plant a bomb near the border.

In Tel Aviv, an Israeli man was killed and 17 people were injured when a truck ran into vehicles and pedestrians. It was not clear whether it was an accident or a deliberate attack. The truck's 22-year-old Israeli-Arab driver said he lost control of the vehicle due to faulty brakes.

• Additional reporting: Phoebe Greenwood

• This article was amended on 17 May 2011. Owing to editing changes the original said that at least two people were killed at Maroun al-Ras after hundreds of protesters broke through Lebanese army barricades to throw rocks across the border. This has been corrected.