A day after mass protests at Israel’s borders set off deadly clashes, Israelis expressed concern that an alarming new chapter had opened in their country’s conflict with the Palestinians.

“The nightmare scenario that Israel has feared since its establishment came true: that Palestinian refugees would simply start walking from their camps across the border, and with their own two feet try to realize the right of return,” wrote Aluf Benn, a commentator in the Haaretz newspaper.

The worry came amid intense scrutiny of Sunday’s clashes, in which Israel’s military used gunfire to repel Palestinian protesters who marched from Syria, Lebanon, the Gaza Strip and the West Bank and breached the frontier in the Golan Heights.

Among Palestinians, there was a sense of satisfaction at what was widely seen as the success of the coordinated protests, which were held on the anniversary of the establishment of Israel in 1948.

“This shows that the occupation can be toppled,” Mahmoud al-Zahar, a leader of the militant group Hamas, said in a telephone interview from the Gaza Strip. “The role of the people has proven itself. Next time, millions will participate.”

The protests, inspired by the uprisings sweeping the Arab world, have conjured up images on both sides of the conflict of waves of dispossessed Palestinians rising up to reclaim homes they lost more than 60 years ago.

Israeli Prime Minister Binyamin Netanyahu, who is scheduled to visit Washington this week amid growing pressure to produce a diplomatic initiative to reinvigorate the peace process, said the protests were aimed at Israel’s destruction.

The demonstrations presented a new type of challenge for the battle-tested Israeli army, which faces the prospect of masses of unarmed protesters, either coming from across the border or from inside the Palestinian territories.

“The Palestinians’ transition from suicide bomber terrorism to mass demonstrations, deliberately unarmed, will confront us with challenges that are not so simple,” Defense Minister Ehud Barak acknowledged in a television interview.

Prompted by the recent upheavals in the Arab world, the Israeli military has been preparing for possible large-scale popular demonstrations by Palestinians in the West Bank and the Gaza Strip, said Brig. Gen. Yoav Mordechai, the army’s chief spokesman.

But soldiers in the Israeli-held Golan Heights were caught unprepared when hundreds of Palestinian protesters from Syria breached a border fence and then tore it down, pelting soldiers with rocks before they were driven back by gunfire, which killed at least two people.

The White House accused the Syrian government of inciting the violence to divert attention from the demonstrations against the Syrian regime. “Such behavior is unacceptable,” press secretary Jay Carney said.

Ten protesters were killed in clashes on Lebanon’s frontier with Israel.

“The barrier of fear has been broken,” Yoav Limor, military correspondent for Israel’s Channel 1 television, told viewers. “The army has to prepare for a new reality and figure out what to do.”

Israeli media reports were filled Monday with mutual recriminations between the army’s intelligence branch and its Northern Command over who was to blame. Newspapers carried images of Facebook pages on which Palestinians were urged to march toward Israeli lines in the Golan Heights and along the Lebanese border on the appointed day. “The Writing was on the Wall,” one headline said.

“What happened?” asked Razi Barkai, the host of a popular talk show on Army Radio, in an interview with Amos Gilad, a top Defense Ministry official. Gilad assured listeners that defense planners had been monitoring Arab social networks for information on planned demonstrations, but he acknowledged that the army was facing a different kind of war.

“This is not classic combat, where you see people advancing and you shoot them,” Gilad said. “Because you achieve the opposite results, and it’s not fitting for a country like ours.”

The Israeli military has experience in confronting unarmed protests. The first Palestinian uprising, which erupted in the late 1980s, pitted youthful stone-throwers against Israeli combat troops, who had to adjust their tactics and weapons, shifting from the battlefield to riot control.

Yet despite years of experience and acquisition of riot gear, the army remains fundamentally unaccustomed to confronting civilian demonstrators, and the prospect that such protests might increase has become a subject of Israeli concern.

Much of the focus is on September, when the Palestinians are expected to seek recognition of a Palestinian state at the United Nations. Israeli officials say they anticipate that the event will prompt large-scale demonstrations.

Sunday’s protests were an annual commemoration of what Palestinians call al-Naqba, or the catastrophe, a reference to their dispersion in the 1948 war that followed the creation of Israel.

Mustafa Barghouti, a Palestinian activist and politician from the West Bank who had marched toward an Israeli checkpoint near Ramallah, said “popular resistance” would gather momentum in tandem with the Palestinian diplomatic push for statehood.

Activists in several Palestinian villages in the West Bank, joined more recently by leaders of the Palestinian Authority, have for several years promoted unarmed grass-roots protests, mostly against Israel’s separation barrier in the area, as the most effective method of confronting Israeli forces.

On online Arab social networks through which Sunday’s protests were organized, people celebrated what one Web site called “the news that shook the Zionist entity.”

One Facebook group member from post-revolutionary Egypt wrote: “I wish I was with them. Not only me, but all the Egyptians that want to liberate Palestine from occupation.”

Special correspondent Samuel Sockol contributed to this report.