An IDF spokesman said that IDF forces securing the border spotted three Palestinians who infiltrated Israeli territory through the security fence and attempted to damage security equipment in the area.
Gaza's health ministry identified two of the casualties as Abdel Rahman Qudeih, 23, and Mohammed Abu Rayda, 20.
"An attempt to infiltrate Israel and sabotage security infrastructure was thwarted", the IDF stated.
The Palestinian rallies, known as the "Great March of Return", will last until May 15, coinciding with the 70th anniversary of Nakba Day (Day of Catastrophe), when Israel was created.
The health ministry said the explosion may have been caused by the handling of explosives.
Hamas has vowed revenge after blaming Israel for an explosion that killed six of its fighters.
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Clevinger went 7 1/3 innings in his first start against the Yankees, setting career highs with 10 strikeouts and 116 pitches. Gray is 3-3 with a 3.38 ERA in eight career regular-season starts against the Indians .
Hamas's Ezzedine al-Qassam military wing brigades said in a statement that the strike was against a border observation post and that nobody was injured in the attack.
Several Palestinians on Saturday placed Molotov cocktails on the security fence before returning to Gaza, the IDF said.
Security officials, speaking on condition of anonymity, and eyewitnesses said that a huge blast occurred in a house of a Hamas militant in the town, which was the result of a bomb that had suddenly exploded.
A military spokeswoman said it was a direct response to a new Palestinian tactic of flying kites with firebombs attached across the Gaza border into Israel to set farmers' fields alight.
Israel says Hamas, the militant group which dominates Gaza, is orchestrating the demonstrations in order to launch attacks.
On May 14, the United States is to move its embassy in Israel from Tel Aviv to Jerusalem, whose Israeli-annexed eastern sector is sought for a Palestinian capital.