The Israeli military says its forces have killed two Palestinian gunmen who unlawfully entered Israel from the Hamas-ruled Gaza Strip on Friday.
Israeli security forces sealed off several Israeli communities along the border, until a gun battle between the suspected militants and Israeli soldiers was over.
The gun battle took place shortly after Israel said it had launched air strikes targeting border tunnels in Gaza, after suspected militants fired at least one rocket into Israel.
The incidents took place a day after U.S. Middle East envoy George Mitchell wrapped up his second round of indirect peace talks between Israel and the Palestinians.
Mitchell met with Palestinian President Mahmoud Abbas on Wednesday and Israeli Prime Minister Benjamin Netanyahu, Thursday, before leaving the region.
Israeli media report the prime minister is preparing to offer a package of goodwill gestures such as releasing Palestinian prisoners and removing some roadblocks in the West Bank.
The Palestinians want a state in areas Israel captured in the 1967 war, with East Jerusalem as a capital. They say they will not return to direct negotiations unless Israel stops building settlements in East Jerusalem and the West Bank.
Mr. Netanyahu has accepted the idea of a Palestinian state, but with conditions and without East Jerusalem.
Israel wants direct negotiations without preconditions.
Some information for this report was provided by AP, AFP and Reuters.