It added that no casualties were caused by the rockets, one of which landed in an open field outside Sderot.
A relative of a Palestinian who was killed at Israeli-Gaza border fence, reacts at the hospital in the northern Gaza Strip September 6, 2019.
Following the Saturday claim of a drone attack, Israeli fighter jets and a drone "struck a number of Hamas military targets, including offensive naval equipment and two military compounds", the army said.
The Palestinian Islamic Jihad said al-Attar was a member in the group's armed wing and was killed in an accidental explosion while trained at one of the military locations belonging to the group in central Gaza Strip, said sources.
An Israeli aircraft targeted the squad that launched the drone, but there were no injuries in that raid.
Later, another infiltrator - this time from northern Gaza - was apprehended, and two knives were found on him, the army said.
Addressing the latest escalation, Israeli Prime Minister Benjamin Netanyahu said he had been updated on the events and threw the blame at Gaza's Islamist rulers.More news: Pakistani astronaut hails India on Chandrayaan-2 mission
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"Hamas is responsible for any act of aggression emanating from Gaza", he said in a statement. "Any attempt to harm our citizens and our soldiers will be met with a forceful response", Netanyahu said in a statement.
Hamas says Israel doesn't honor the agreement.
A delegation from Egypt arrived in the Gaza Strip on Sunday to mediate between the Hamas movement ruling the enclave and Israel as tensions mounts between the warring sides.
Israeli forces said thousands of Palestinians took part in demonstrations along the border.
Palestinians have been holding often weekly protests along the fortified border fence since March 2018. Seventy protesters were wounded, 38 of them by live fire, medical officials said.
Two Palestinian teenagers have been killed by Israeli gunfire during a protest along the Israel-Gaza border fence.
The truce was negotiated by Egyptian and United Nations officials with aid from Qatar to end several severe flare-ups of violence in recent months.