The soldiers shot across the border into Gaza after the Palestinians came too close to the Israeli frontier, throwing stones and rolling burning tyres, an army spokeswoman said. Gaza medics said six people were killed and 50 wounded.
The protests were in solidarity with Palestinians in Jerusalem and the Israeli-occupied West Bank, where tensions have surged in 10 days of violence in which four Israelis and at least eight Palestinians have been killed.
Palestinians have been angered by events at the al-Aqsa mosque compound in Jerusalem's Old City and fear Israel wants to change the status quo at the holy site, revered by Muslims as the Noble Sanctuary and by Jews as the Temple Mount.
Israeli Prime Minister Benjamin Netanyahu has denied wanting to change conditions under which Jews are allowed to visit the site but non-Muslim prayer is banned. His assurances have done little to quell alarm among Muslims across the region.
The violence is not of the intensity of two Palestinian uprisings in the late 1980s and early 2000s but the attacks have prompted talk of a third "intifada".
Both Netanyahu and Palestinian President Mahmoud Abbas have called for calm and Palestinian police continue to coordinate with Israeli security forces to try to restore order, but there are few signs of the tension and violence dying down.
In Gaza, Hamas leader Ismail Haniyeh praised Palestinians who have carried out knife attacks as "heroes" and said a new intifada focused on Jerusalem was underway.
"This is Friday, this is the day of rage... It is a day that will represent the start of a new intifada in all of the land of Palestine," he told followers after prayers.
"We give our souls and blood for Jerusalem, Jerusalem and al-Aqsa is part of the religion."
Earlier on Friday, a Jewish assailant stabbed four Arab men in the southern Israeli city of Dimona, an attack denounced by Netanyahu and described by one of his ministers as "terrorism".
In the northern city of Afula, an Israeli-Arab woman was shot several times and wounded by police who closed in on her as she held up a knife, a video clip circulated on social media showed. Police said she had tried to stab a bus station guard.
In the Old City of Jerusalem, a Palestinian stabbed and wounded a 14-year-old Jewish boy, and near a Jewish settlement in the West Bank city of Hebron, a Palestinian stabbed an Israeli policeman before being shot dead.
There was also violence in the West Bank city of Ramallah, with video footage showing an Israeli army jeep running over a stone-throwing Palestinian, who was wounded. Medics said 247 Palestinians were hurt in Friday's West Bank disturbances.
NO TALKS, NO PEACE
Rancour runs deep between Israel and the Palestinians, whose last round of negotiations ended in April 2014 without progress.
A new intifada would further complicate efforts by world leaders to resolve conflicts in Syria, Iraq and Yemen, and there is little appetite to re-engage in peace efforts between Israel and the Palestinians after many failures in the past.
The chances of talks resuming before U.S. President Barack Obama's term ends appear slim. His senior aide, Ben Rhodes, told Israeli radio on Thursday that Washington had no "silver bullet" to bring about the envisaged Palestinian state alongside Israel.
Netanyahu has accused Abbas, his Fatah party and the Islamist group Hamas of inciting the violence in East Jerusalem in recent weeks. He reiterated that message at a news conference on Thursday, adding that there was no "quick fix".
"We are in the midst of a wave of terrorism with knives, firebombs, rocks and even live fire," he said.
"While these acts are mostly unorganized, they are all the result of wild and mendacious incitement by Hamas, the Palestinian Authority, several countries in the region and... the Islamic Movement in Israel."
Abbas has praised Palestinians for "defending" al-Aqsa but also urged people to engage in "peaceful popular resistance".
As well as tensions over al-Aqsa, Palestinian anger has mounted as Israeli forces have taken a tougher line against protesters who are violent. Netanyahu has told troops and police they can shoot Palestinian stone-throwers if they have reason to believe an Israeli life is threatened. Israeli mayors have encouraged residents with gun licences to carry their weapons.
There is also frustration at the failure of Israeli police to track down the Jews suspected of an arson attack on a Palestinian family in the West Bank two months ago in which a child and his parents were killed.
In turn, Israelis are on edge after deadly stone-throwing attacks by Palestinians and the killing of an Israeli couple in the West Bank 10 days ago. They were shot as they drove in their car with their four children.
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