Sources said he would explore the possibility of brokering a ceasefire amid news that Israel was calling up thousands of reservists ahead of a possible ground invasion.
Netanyahu agreed to an Egyptian request to "cease all offensive operations" during the visit, a senior government official said, on the condition Hamas held its fire.
Last evening, 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 a suburb south of the city.
Two days of Israeli air strikes have killed 19 Palestinians, including seven militants and 12 civilians, among them six children and a pregnant woman. A Hamas rocket killed three Israelis in the town of Kiryat Malachi yesterday morning.
The latest upsurge in the long-running conflict came on Wednesday 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.
Israel says its offensive responded to increasing missile salvoes from Gaza. Its bombing has not yet reached the saturation level seen before it last invaded Gaza in 2008, but Israeli officials have said a ground assault remains possible. The Gaza conflagration has stoked the flames of a Middle East ablaze with two years of Arab popular revolution and a civil war in Syria that threatens to spread farther afield.
Israeli warplanes bombed targets in and around Gaza City. In a hint of escalation, the spokesman for Israel's military said it had received the green light to call in up to 30,000 reserve troops. Egypt's new Islamist president, Mohamed Mursi, viewed by Hamas as a protector, led a chorus of denunciation of the Israeli strikes by allies of the Palestinians.
Mursi faces domestic pressure to act tough. But Egypt gets $1.3bn (¤1bn) a year in US military aid and looks to Washington for help with its ailing economy, constraining Mursi despite his need to show Egyptians that his policies differ from those of his US-backed predecessor, Hosni Mubarak.
Air raid sirens sent residents running for shelter in Tel Aviv, a Mediterranean city that has not been hit by a rocket since the 1991 Gulf War.
"This escalation will exact a price that the other side will have to pay," Israeli Defence Minister Ehud Barak said in a television broadcast shortly after the strike.
But an Israeli cabinet statement on Wednesday spoke only of "improving" national security -- acknowledgement that the Jewish state had no illusions about crushing the militants once and for all.