After a deadliest day of violence killed 55 and wounded 2,700 Palestinians, Israeli Prime Minister Benjamin Netanyahu said his military acted in self-defence against Gaza's Islamist rulers, Hamas, who he said wanted to destroy Israel, the media reported.
The violence on Monday coincided with the dedication ceremony for the US embassy. The transfer of the US embassy from Tel Aviv had incensed Palestinians, who already claim eastern Jerusalem as the capital of a future Palestinian state.
Netanyahu defended his military, saying: "Every country has an obligation to defend its borders.
"The Hamas terrorist organisation declares its intention to destroy Israel and sends thousands to breach the border fence in order to achieve this goal. We will continue to act with determination to protect our sovereignty and our citizens."
An Israel Defence Forces (IDF) spokesman said soldiers fired on those engaged in "terrorist activity and not on demonstrators, who were dispersed by usual means such as tear gas and according to the rules of engagement".
Palestinians were demonstrating on Monday as they have been for six weeks as part of a protest, orchestrated by Hamas, called the "Great March of Return".
However, Monday's protests, and more planned for Tuesday, were the culmination that mark the anniversary of Israel's creation in 1948, and what Palestinians term the 'Nakba' or Catastrophe.
It refers to the hundreds of thousands of Palestinians, who subsequently fled their homes or were displaced in the war that followed, the BBC said.
Hamas said the border protests were being stepped up for Tuesday.
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