Gaza’s health ministry also reported that some 408 Palestinians had been taken to hospitals and medical centres for treatment. The dead included a 16-year-old, it said.
Palestinians burned mounds of tyres and threw stones at Israeli soldiers over the border fence, who responded with tear gas and live fire.
Israel said there were also attempts to break through the barrier.
Thousands of protesters — Israel estimated 20,000 — gathered in locations near the border east of Khan Yunis, in the south of the blockaded Palestinian enclave, and east of Gaza City, among other spots.
The number of protesters was however lower than last week, when a demonstration by tens of thousands led to clashes in which Israeli forces killed 19 Palestinians.
The tyre fires were meant to be a smokescreen from Israeli snipers, and thick black smoke covered the border area in some places.
Israeli forces took up positions on the other side of the border and set up large fans in a bid to push away smoke.
They also used water cannon to try to douse flames.
Hamas’s leader in Gaza, Yahya Sinwar, hailed the protests and condemned Israel’s blockade of the Gaza Strip.
“They said Gaza would give up its principles, its project of liberation and (dream) of return if they starve it, but Gaza is coming out today,” he said to protesters east of Khan Yunis.
He referred to the protest’s call for Palestinian refugees to be able to return to land they fled or were expelled from in what is now Israel.
Sinwar said Gazans would “break the border and return to our land and pray in Jerusalem.”
Israel’s military said some 20,000 Palestinians were “rioting” and “attempts were made to infiltrate into Israel under the cover of a smoke screen.”
It also said explosive devices and firebombs were thrown, adding that soldiers opened fire “in accordance with the rules of engagement.”
Mona al-Shaar, 43, who was distributing bottles of vinegar to protesters east of Khan Yunis to dab onto tissues to help them cope with tear gas, said that “we came here for the land and for a better future.”
“The Israelis are cowards.”
Israel had warned that its open-fire rules would remain unchanged for Friday’s protests, pledging to stop damage to the fence and prevent infiltrations or alleged attacks.
It had faced mounting criticism over its use of live fire, and UN chief Antonio Guterres called for restraint ahead of Friday’s protest.
“I particularly urge Israel to exercise extreme caution with the use of force in order to avoid casualties,” he said.
In the March 30 demonstration, a number of protesters strayed from the main demonstration and approached the heavily fortified fence on the border with Israel.
Israel says troops opened fire only when necessary against those throwing stones and firebombs or rolling burning tyres at soldiers.
It said there were attempts to damage the fence and infiltrate Israel, while alleging there was also an attempted gun attack against soldiers along the border.
Israel accuses Hamas, the Islamist movement that runs the Gaza Strip and with whom it has fought three wars since 2008, of using the protests as cover to carry out violence.
But the toll of those killed and wounded on March 30 — more than 750 people were injured by gunfire, according to Gaza’s health ministry — led to criticism of Israel.
There were no Israeli casualties.
Palestinians say protesters were shot while posing no threat to soldiers, and unverified videos that have spread online have fuelled their accusations.
The videos include one appearing to show a man with a tyre shot while running away from the fence.
Human Rights Watch has called the actions by the Israeli soldiers “calculated” and illegal.
Guterres and the European Union have called for an independent investigation, which Israel has outright rejected.
Israel says more than half of the dead from the previous Friday were members of militant groups, including the armed wing of Hamas.
Hamas’s armed wing has claimed only five of them, saying they were participating “in popular events side-by-side with their people”.
Militant group Islamic Jihad has claimed at least one of the dead as a member, but it said he was not carrying a weapon when he was shot.
Hamas has meanwhile offered compensation of $3,000 to the families of protesters killed and $500 for those seriously injured, drawing outrage from Israel.
The protests, designed to last six weeks, are in support of refugees.
More than 700,000 Palestinians fled or were expelled from their lands during the war surrounding Israel’s creation in 1948.
Israelis say allowing the so-called “right of return” would mean their country would cease to exist.
Protests will run until the expected opening of the new US embassy in Jerusalem in mid-May.
The US move has led to deep anger among Palestinians, who see the annexed eastern sector of Jerusalem as the capital of their future state.
The White House on Thursday refrained from criticism of Israel and called on protesters to remain peaceful.