While the Israelis have rejected criticism that their response to the protests has been disproportionate, the Israeli military appeared to be treating the killing of Ms. Najjar as a case that required further scrutiny.

Thousands of people attended the funeral of Ms. Najjar in Gaza on Saturday. A group of United Nations agencies issued a joint statement expressing outrage at the killing of an unarmed medical relief worker.

Witness accounts said Ms. Najjar was shot two or three times in the upper body by Israeli soldiers positioned across the fence as she was seeking to aid an injured protester, about an hour before dusk on Friday.

The Israeli military’s Twitter post, which misstated her age as 22, said an initial examination had found “that a small number of bullets were fired during the incident, and that no shots were deliberately or directly aimed towards her.”

A follow-up Twitter post said the episode would be further examined by the Israeli military and that the findings would be passed to the chief military lawyer.

The protests along the fortified fence that separates Gaza from Israeli territory have become an acute flash point in the intractable Israeli-Palestinian conflict.

The Palestinians have been rallying at the fence every Friday since the end of March, protesting an 11-year-old blockade of Gaza and demanding the right to return to lands that are now part of Israel.

A resolution presented to the United Nations Security Council on Friday to condemn the Israeli actions at the Gaza fence was vetoed by the United States, which contended the wording was one-sided against its Middle East ally.