Rockets fired from Gaza have hit several sites in southern Israel shortly after Egyptian Prime Minister Hisham Kandil arrived in the Palestinian enclave on Friday, reportedly to try to broker a ceasefire.
The Israeli air force responded with an attack on the house of Hamas's commander for southern Gaza, according to a Hamas source.
Israel had announced it would suspend military operations in Gaza during Mr Kandil's three-hour visit so long as Hamas also halted all fire.
Israel has started drafting about half of its 30,000 reserve troops in a sign that violence could escalate further with militants in the Gaza Strip.
Israel's two-day assault on Gaza has largely been from the air, but officials have said a ground incursion could be necessary to stem rocket fire into southern Israel.
Sources told Reuters Mr Kandil would explore the possibility of brokering a ceasefire.
A senior Israeli government official says Prime Minister Benjamin Netanyahu had agreed to an Egyptian request to cease all offensive operations in Gaza during the Egyptian leader's three-hour visit, on the condition there was no fire from Gaza into Israel during that period.
The latest upsurge in the long-running conflict came earlier this week when Israel killed Hamas' military mastermind, Ahmed al-Jaabari, in a precision air strike on his car.
Israel then began shelling the coastal enclave from land, air and sea.
The total Palestinian casualties so far from two days of Israeli air strikes are 19 dead, including seven militants and 12 civilians, among them six children and a pregnant woman.
A Hamas rocket killed three Israelis on Thursday in the town of Kiryat Malachi, and two rockets from Gaza crashed near Tel Aviv in the first such attack on Israel's commercial capital in 20 years.
One fell into the Mediterranean Sea and the other in an uninhabited part of one of the Tel Aviv suburbs south of the city.