Israeli military officials had warned Palestinians to steer clear of the fence Friday and deployed drones and sharpshooters.

But the Israeli military said at least 10,000 people demonstrated in five locations. Some attempted to damage security infrastructure, including with firebombs and an explosive device, the army said. At one point, the protesters tried unsuccessfully to fly a firebomb over the border with a kite.

Demonstrators burned tires at the border, emitting large plumes of black smoke. It was a tactic, protesters said, to shield themselves from Israeli sniper fire.

Some Palestinians, mostly young men, approached the border area east of Gaza City — where an expanse of empty farmland is interrupted by barbed wire and Israeli watchtowers — and some used catapults to send rocks flying over the 10-foot-high fence.

Since the demonstrations began last month, Israeli forces have killed at least 28 Palestinians, according to local health officials.

The demonstration on Friday was smaller than in the previous two weeks, and the death toll was lower, with the Palestinian health ministry in Gaza reporting one death, that of 28-year-old Islam Herzallah, who died of a gunshot wound to the abdomen.

The health ministry said that at least 968 people were wounded by gunfire and tear gas Friday. The figures could not be independently verified.

Rights groups have slammed the Israeli response to the demonstrations, criticizing what they say is an excessive use of force against unarmed protesters.

“The Israeli authorities must put an immediate end to the excessive and lethal force being used to suppress Palestinian demonstrations in Gaza,” Amnesty International said in a statement Friday. It called for an independent investigation into the military’s conduct.

Israel has accused Palestinian militants of using the protests as cover for attacks.

Farther from the frontier on Friday, families picnicked under tents and listened to speeches and nationalist songs that blasted from loudspeakers. Senior officials from the militant Hamas movement that rules Gaza toured the area but stayed several hundred meters from the border.

The group, which Israel and the United States consider a terrorist organization, has helped organize the protests. They began last month to draw attention to the plight of Palestinians living in Gaza, which the United Nations has said is on the verge of economic collapse.

The protests also have been billed as an effort by Palestinian refugees to claim their right of return. The majority of Gaza’s 1.8 million residents are descendants of refugees who lost their land when Israel was established in 1948, and many live in cramped refugee camps that now resemble shantytowns.

“We need a solution,” said 29-year-old Mahmoud, who was on crutches after he was shot in the leg at a demonstration on April 6. “We have no work, no security. We are miserable.”

About 80 percent of Gazans rely on international assistance, including food aid, the United Nations says. And the World Bank puts Gaza’s unemployment rate at 41 percent. Trade restrictions imposed by Israel and Egypt, which shares a border with the Gaza Strip, have hampered economic growth. A lack of fuel also means that Gazan households receive only a few hours of electricity per day.

Israel and Hamas have fought three wars in the Gaza Strip since 2009. In the last conflict, in 2014, more than 2,100 Palestinians were killed, according to the United Nations. Sixty-six Israeli military personnel were also killed, along with six Israeli civilians and a Thai national.

The Israeli army said Friday that it had deployed more troops to the border.

A military official who briefed journalists showed footage of a Palestinian gunman approaching the fence to plant an explosive device. It was unclear, however, if the incident took place as part of the demonstrations. Israel says it has seen an uptick in attempted attacks since the protests started March 30.

“We do not shoot to kill anyone, only those who are with weapons,” the military official said.

East of Gaza City on Friday, in the area of Zeitoun, dozens of ambulances screamed past demonstrators, ferrying the wounded to a nearby field clinic. There, 11 doctors and other medical workers treated the injured in a makeshift tent.

The majority of victims were treated for tear-gas inhalation, the clinic’s manager, Khalil Siam, said. The remaining injuries included gunshots to the legs and wounds from rubber-coated steel bullets.

“Even if I lose my neck, I will fight to get our land back,” said one of the wounded, 30-year-old Wael Abu Zuweida. A street vendor with a wife and child, Abu Zuweida was injured when a bullet grazed his thigh.

“This is the second week in a row he is here,” one medic said to chuckles from colleagues as Abu Zuweida was pulled from an ambulance. He suffered a similar injury at the April 6 demonstration.

“God will protect us,” Abu Zuweida said, as he limped back to the protest with a friend.

Correction: An earlier version of this article mistakenly said the Israeli military had deployed tanks, but a military spokesman confirmed that it did not use tanks.

Eglash reported from Kerem Shalom, Israel. Hazem Balousha in Zeitoun contributed to this report.