Israeli forces say they were met with heavy resistance from Hamas when they pounded multiple sites across the Gaza Strip.
Israel has resumed air strikes on Gaza following Hamas's rejection of an Egyptian-proposed Gaza ceasefire.
Egypt's campaign to shut down smuggling tunnels running under its border into the Gaza Strip threatens to throw thousands of Palestinians out of work.
The UN chief has called for an immediate ceasefire in the Gaza Strip and the US Secretary of State has headed to the region with a peace message.
There are theories among Israelis and Palestinians about what has propelled the two sides towards their second war in four years.
The Hamas government has barred much of Gaza's fruit imports from Israel, citing a need to cultivate local Palestinian agriculture.
Previous ceasefire deals after earlier rounds of fighting have often got off to a slow start with guns falling silent within a day or two.
Israeli Gilad Shalit has been freed after years as a Hamas prisoner, as hundreds of Palestinians exchanged for him received a hero's welcome in Gaza.
Israel killed four Palestinian militants and wounded half a dozen others as it pursued air raids in Gaza for a third day on Saturday.
Militant groups in the Gaza Strip said on Thursday they had joined forces to step up attacks against Israel, possibly including suicide bombings.