Gaza health authorities say at least 15 other Palestinians, including a child, were wounded by Israeli fire.
Israeli aircraft have hit several targets in the besieged Gaza Strip after rocket launches towards Israel, marking the third consecutive night of hostilities.
The Israeli military said it launched attacks on Hamas targets early on Monday following incoming rocket fire late on Sunday. There were no immediate reports of casualties on either side.
According to an Israeli military statement on Twitter, the targets included four Hamas compounds used for military training, a weapons workshop and the entrance to an underground tunnel.
Hazem Qasem, a spokesman for Hamas, the Palestinian group which governs Gaza, told Al Jazeera the attacks were a response to the escape last week of six Palestinian inmates from a maximum-security Israeli prison. Two of them remain on the run while the others have been rearrested.
“The Israeli occupation is trying to weaken the Palestinian morale and instil fear of a possible escalation by bombing Gaza,” he said.
Qasem said that any escalation – including the potential killing of the two prisoners still on the run or any further raids in the Jenin camp – would not be tolerated.
The latest round of hostilities escalated on Friday, when sirens warning of rocket fire sounded in southern Israel, hours after Israeli police rearrested two of the prisoners affiliated with the Palestinian Islamic Jihad group.
The Israeli air raids on Monday came after three separate rocket launches from the Gaza Strip, at least two of which were intercepted by Israel’s defence systems.
One rocket was intercepted on Sunday night over the southern city of Sderot, where five residents were lightly wounded, The Jerusalem Post reported.
Israel’s foreign minister proposed on Sunday a development plan to improve living conditions within the enclave, where some two million people live, in exchange for a cessation of the hostilities.
Yair Lapid offered to repair the electricity system, build a water desalination plant and bring significant improvements to the healthcare system. “In exchange, Hamas will commit to long-term quiet,” he said.
The foreign minister said his plan does not yet amount to official policy in Israel’s eight-party coalition government but had support from Prime Minister Naftali Bennett.
Attempts to broker a long-term truce have been hampered by the inability to agree on a system to renew Qatari payments to needy Gaza families that guarantees that the funds are not diverted towards Hamas for military use.
Qatari stipends for civil servants and poor families were suspended in May, when Israel and Hamas fought a full-scale war, the fourth since 2008.
The United Nations Middle East envoy said it would begin distributing cash aid to thousands of poor families in the besieged Gaza Strip on Monday under a programme funded by Qatar, delivering aid to nearly 100,000 beneficiaries.
The UN High Commissioner for Human Rights said Israeli air raids on the territory had resulted in “the widespread destruction of civilian infrastructure”.
Israel and Egypt have maintained a blockade on Gaza for 14 years, tightly controlling the movement of people and goods in and out of the territory.
Maram Humaid contributed reporting from Gaza.