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

Brig. Gen. 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 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.

In the days leading up to the 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, some threw rocks at Israeli soldiers. The Israeli military said that tires were set alight and molotov cocktails were also thrown.

Gaza has been under blockade by Israel for more than a decade.

and accused Hamas of using the demonstration as a cover to carry out “terror attacks.”