GAZA CITY, Gaza Strip >> For weeks, Palestinians protesting along the fence between Gaza and Israel have conjured up the idea of swarming across the barrier all at once, a mass of hundreds of thousands of people too numerous for Israeli soldiers to arrest or even to shoot.

And Israelis have been worrying aloud about what their soldiers would do in response.

Today both sides got a small sense of what that could mean when hundreds of Palestinians, urged on by a Hamas leader in a fiery midafternoon speech, rushed the security barrier at the eastern edge of Gaza City and tried to cross into Israel.

Dozens made it through a barbed-wire barrier about 30 yards inside Gaza territory, deploying wire cutters, hooks and winches. Israeli troops opened fire with a mix of live ammunition and rubber bullets, killing three people and wounding nearly 1,000 more, according to Gaza health officials.

“That was the first time we’ve seen this kind of synchronized and focused attack on the fence, and it’s something we are not going to tolerate by any stretch,” said Lt. Col. Jonathan Conricus, a spokesman for the Israeli military. “It was a very swift move, and it seemed to be very focused. It looked as if they were disregarding the danger that they were facing.”

The protest was the fifth in a series of demonstrations organized by Hamas, the Islamic group that rules Gaza. It has succeeded in ways that firing missiles into Israel has not, drawing international sympathy and attention to the Palestinian cause and the claims of the right of return for Palestinian refugees into what is now Israel.

The protests are expected to continue for three more weeks, and with neither side giving ground they appear to be headed for more violence. Already more than 40 people have been killed.

Just after midnight Saturday, Israel said its fighter jets had struck six naval targets belonging to Hamas in Gaza in retaliation for the attacks on the barrier fence.

The breach of the fence was no mere protest: Those assaulting it threw firebombs and rolled burning tires at the fence to try to melt it; at least some carried pistols, according to both the Israeli military and Palestinian witnesses.

Four Palestinian protesters said they saw two men with handguns fire at Israeli soldiers and then flee. The soldiers threw a hand grenade in response, the witnesses said, wounding other people, two of them critically.

These accounts could not be verified and two other Palestinians disputed them, saying the people with handguns did not fire them. The Israeli military did not confirm that it had been fired on.

A 21-year-old man who gave his name only as Ahmed said he had seen five men shot as they pulled away part of the barbed-wire barrier, which amounts to the Israelis’ first line of defense.

When some were shot, others came forward.

For the first time in five weeks of protests, some reached the second barrier — an electrified, sensor-laden fence that marks the edge of Israeli territory — and tried to climb it or pull it down. A few hundred yards beyond it lies the Israeli farming community of Nahal Oz.

Ibrahim Shahin, 26, said he was among a group of about 12 men who cut through the barbed wire and then began climbing the electrified fence. He said he saw an Israeli soldier firing “randomly” at the group and added that three men were shot in the head. Another, he said, was shot in the abdomen and wounded.

“One of them, his last breath was on my shoulder,” he said, his T-shirt soaked in blood.

One Israeli soldier threw a grenade at the group, he said. Asked how he had avoided injury, he added, “I was lucky.”

The protest is meant to culminate on May 15, when Palestinians mark the 70th anniversary of the Nakba — the “catastrophe” of Israel’s establishment and of the displacement of hundreds of thousands of their forebears who were expelled or fled from their homes.

Hamas has called the protests peaceful, despite the Molotov cocktails thrown at Israeli soldiers and firebombs attached to kites that are routinely sailed over the fence, setting fires to Israeli farmland. Israel, defending its use of deadly force, has described the protests as riots that could turn into an invasion at any time.

The Israeli military acknowledged that it was surprised by the speed and tenacity of the assault, and by its location.

Conricus said that Friday’s crowds totaled 12,000 to 14,000. Around 5 p.m., when the protest seemed to be winding down uneventfully, he said, “between 500 and 700 rioters assaulted the fence in a way that we have not seen them assault it before.”

He said the effort to breach the fence “shows exactly what we are talking about.”

“This is not a peaceful demonstration,” he said. “There’s nothing serene about this. They’re trying to infiltrate into Israel, damage our infrastructure and kill Israelis.”

Reminded that Israel’s critics have denounced the country for attacking unarmed demonstrators with deadly force, Conricus said: “They aren’t the ones defending Israeli citizens from a hateful mob of thousands of Palestinians. It doesn’t matter if someone is carrying flowers if he’s tearing down the fence. That’s a violent threat.”

Friday’s demonstration at the eastern edge of Gaza City — adjacent to the old Karni Crossing, a cargo terminal that allowed goods to cross between Israel and Gaza until it was shut down in 2011 — had been largely peaceful until late in the afternoon.

But then the senior Hamas leader Ismail Radwan gave a rousing speech, urging the protesters not to fear death but to welcome martyrdom.

“When we are brave, we are getting closer toward martyrdom, martyrdom, martyrdom,” he said.

Thousands began streaming toward the barrier fence, setting off a tremendous barrage of tear gas from the Israeli side that did not deter many.

Radwan thundered on: “We say to Nikki Haley, to Netanyahu, to the criminal Lieberman” — referring to the United States ambassador to the United Nations, the Israeli prime minister and Israel’s defense minister, Avigdor Lieberman — “we are afraid neither of death nor of martyrdom.”