The organizers had been purposely vague about plans to breach the border, to keep Israel guessing.

The Israeli mainstream has largely backed the army, though there has been criticism.

“I categorize what happened as a failure,” said Shlomo Brom, a retired brigadier general now at Israel’s Institute for National Security Studies. “The Palestinian aim was to raise international consciousness, and to put the Palestinian issue back on the international and Israeli agenda. It succeeded.”

While the military probably also decided to use lethal force as a deterrent, Mr. Brom said, “In my opinion they should have planned from the beginning to use minimal force and to prevent casualties.”

Mkhaimar Abusada, a professor of political science at Al-Azhar University in Gaza, said that from what he had heard there was no plan to cross the border. “It was a mass Palestinian nonviolent protest against Israel, and to approach the border area,” he said. “But when you have large crowds you cannot control — so yes, some tried to infiltrate the borders between Gaza and Israel.”

Ahmed Abu Artema, a Gazan social-media activist who initiated the protest, said by telephone on Sunday that the idea of returning to the lands lost in 1948 was a “strategic goal” that would “not necessarily be achieved within a month or a year,” but that the protesters along the borders would determine the timing.

Hamas, which quickly adopted the return campaign, played a large role in orchestrating it. The Islamic group, which is classified by much of the Western world as a terrorist organization, said five of those killed belonged to its military wing, but said they were participating in the protest “side by side” with their people.