JERUSALEM — Israel’s military warned Saturday that it will step up its response to violence on the Gaza border if it continues, even as the United Nations said it was ‘‘deeply concerned’’ and called for an investigation after at least 15 Palestinians were killed during demonstrations.

Brigadier General Ronen Manelis, Israel’s chief military spokesman, said it had so far restricted its actions to the border fence but would go after militants ‘‘in other places’’ if attacks continue, the Associated Press reported.

Tens of thousands of Gaza residents massed at points on the border with Israel on Friday in what was billed as a peaceful ‘‘March of Return’’ to mark Land Day, the anniversary of the Israeli appropriation of Arab-owned land in the Galilee area in 1976.

But the day descended into the bloodiest in Gaza since the 2014 war between Israel and Hamas, the Islamist militant group that controls the enclave. More than 700 people suffered gunshot wounds after Israeli sharpshooters deployed to the border opened fire with live ammunition.

Hamas said Saturday that four of the 15 dead were members of its military wing. It said a fifth member who was not on the Health Ministry list was killed near the border, and that Israel has the body. It said another man is also missing in the border area.

The violence dropped significantly Saturday as just small groups of Palestinians threw stones in several areas near the fence, drawing Israeli fire that injured 25 people, the AP reported, citing the Gaza Health Ministry.

In the days leading up to Friday’s demonstration, the military had warned that anyone approaching the border fence would be in danger. Men, women, and children gathered, and while many demonstrated peacefully, waving Palestinian flags, some threw rocks at Israeli soldiers across the fence.

The Israeli military said that tires were set alight and firebombs were thrown, and accused Hamas of using the demonstration as a cover to carry out ‘‘terror attacks.’’ It said two militants opened fire in one incident on the northern border, after which it responded with tank fire and airstrikes.

Israeli human rights group B’Tselem said Israel’s response to unarmed protesters was ‘‘illegal.’’

United Nations Secretary-General António Guterres is ‘‘deeply concerned’’ about the border clashes, a statement from his office said.

‘‘He also appeals to those concerned to refrain from any act that could lead to further casualties and in particular any measures that could place civilians in harm’s way,’’ it continued, adding that the UN chief had called for an ‘‘independent and transparent investigation into these incidents.’’

Manelis said all those killed were engaged in violence.

Hamas and other Palestinian factions that called for the demonstrations hope to sustain them for another month and a half, culminating with the anniversary of Israel’s independence, known to Palestinians as the ‘‘Nakba’’ or catastrophe.

The opening of the US embassy, also slated for the anniversary, is expected to add further fuel to protests. Meanwhile, a growing sense of hopelessness for Gazans amid a humanitarian crisis, has spurred on demonstrators, some of whom say they have little to lose.

Gaza has been under blockade by Israel for more than a decade, since Hamas took control of the territory in 2007. Israel cites security reasons for only allowing a tiny proportion of its 2 million residents to leave, even to travel to other Palestinian areas in the occupied West Bank.

It is estimated that the unemployment rate is pushing 50 percent, a figure that is higher among the 140-square-mile strip of territory’s youth.

A feud between Hamas and the Palestinian Authority, which is based in the West Bank city of Ramallah, has compounded misery for Gazans. The Palestinian Authority has cut salaries to its employees in Gaza as it attempts to squeeze Hamas, while reconciliation efforts brokered by Egypt have broken down.

‘‘I want to be shot,’’ said 22-year-old Yahya Abu Assar at the demonstrations on Friday. ‘‘I don’t want this life.’’

Israeli Prime Minister Benjamin Netanyahu congratulated the soldiers Saturday for allowing the rest of the country to celebrate the Passover holiday safely.

‘‘Israel is acting determinedly and decisively to protect its sovereignty and the security of its citizens,’’ he said.

Passover began Friday night, on the same day that Christians observed Good Friday.

The border protests against Israel were seen as a new attempt by Hamas to break the border blockade, imposed by Israel and Egypt after the group seized Gaza in 2007 from forces loyal to its rival, Palestinian President Mahmoud Abbas. The continued closure has made it increasingly difficult for Hamas to govern.

Life in the coastal strip has deteriorated further in recent months, with rising unemployment, grinding poverty, and daily blackouts that last for hours.

The prospect of more protests and Palestinian casualties in coming weeks could also place Israel on the defensive.