Medical officials in Gaza say an Israeli air strike on a vehicle has killed a Palestinian militant.
The officials say at least three other people were wounded in the strike Monday in Rafah, near the Egyptian border.
Israel bombed Hamas targets in the Gaza Strip, hours after its Cabinet on Sunday threatened a "harsh and disproportionate" response to new Palestinian rocket and mortar attacks into southern Israel.
Hamas said Israeli aircraft bombed an unoccupied police station and at least six tunnels, which are used to smuggle weapons and goods from Egypt into the Palestinian enclave.
Earlier, Palestinian militants fired at least seven rockets and mortar shells into Israel, wounding two people.
Hamas has not taken responsibility for, or condemned, the new attacks. Some of the attacks have been claimed by members of the militant al-Aqsa Martyrs Brigades.
Hamas demanded that Israel open its border crossings with Gaza as part of a cease-fire.
Israel said that will not happen until Hamas releases a captive Israeli soldier held in Gaza for two and a half years.
Also Monday, Egypt began installing surveillance cameras and motion sensors on its border with Gaza as part of efforts to crack down on tunnels used by weapons smugglers.
The Egyptian government is trying to work out a long-term truce acceptable to both sides. It also is trying to reconcile Hamas with the Palestinian Authority, which Hamas ousted from Gaza in 2007.
Palestinian President Mahmoud Abbas is in Cairo Monday for discussions with Egyptian leaders. He will then go to France. A Hamas delegation also is in the Egyptian capital for talks.