After Israeli Prime Minister Benjamin Netanyahu defended the military action that killed 55 Palestinians and wounded 2,700 as "self-defence", Palestinian Authority President Mahmoud Abbas called for intensified protests on Tuesday, the media reported.
Netanyahu defended his military against Gaza's Islamist rulers, Hamas, who he said wanted to destroy Israel, and said: "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."
Following the deadliest day of violence since the 2014 Gaza war, Abbas called Palestinians to intensify their protests on Tuesday. Announcing three days of mourning, he said: "Today (Monday) once again, the massacres against our people continue."
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".
It relates to the occasion of Nakba Day, (catastrophe in Arabic), referring to the mass expulsion of Palestinians both before and after the founding of the state of Israel in 1948.
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.
Israel on Monday said some 40,000 Palestinians had taken part in the "violent riots" at 13 locations along the Gaza Strip security fence, the BBC reported.
Palestinians hurled stones and incendiary devices, while the Israeli military used tear gas and live fire from snipers, the BBC reported.
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".
There were clashes between Israeli police and protesters who raised Palestinian flags outside the new embassy in Jerusalem and several protesters were detained.
Hamas said the border protests were being stepped up for Tuesday.
Palestine Liberation Organisation Executive Committee member Wasel Abu Yousef told Efe that Tuesday's strike would protest the "massacre" of Palestinians in Gaza.
More protests in the West Bank were expected for Tuesday, including a morning rally, with demonstrators scheduled to move toward the Beit El military checkpoint.
For the afternoon there would be another rally in which candles would be lighted to represent each Palestinians killed on Monday in Gaza, he added.
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