At least a dozen people have been killed by airstrikes on the Gaza Strip over the past 24 hours, Palestinian officials said, as Israel threatened a lengthy offensive against militants whose rocket fire reached as far as Tel Aviv.
The Israeli airstrikes were heavy - 150 targets were hit on Tuesday - and the Jewish state is threatening a ground invasion, with the cabinet authorising the call-up of 40,000 reservists.
Meanwhile, Israelis ran for cover as sirens sounded in Jerusalem and Tel Aviv as militants launched their deepest attack from Gaza since hostilities flared three weeks ago.
The Israeli military said its Iron Dome anti-missile system shot the Tel Aviv rocket out of the sky.
Israel said a ground invasion of the Gaza Strip was possible, but not imminent, and it urged citizens within 40 kilometres of the enclave to stay close to bomb shelters.
"We are preparing for a battle against Hamas which will not end within a few days," said defence minister Moshe Yaalon.
"We will not tolerate missiles being fired at Israeli towns and we are prepared to extend the operations with all means at our disposal in order to keep hitting Hamas."
Explosions echoed across the densely populated Gaza Strip, shaking buildings and sending plumes of smoke into the air.
In residential areas, the crying of children could be heard as ambulance sirens wailed.
At least eight civilians were among the dead, Palestinian government and medical officials said.
On the Israeli side, rocket impacts wounded at least two people, medics said.
In the Israeli port city of Ashdod, motorists scrambled from their cars and raced for the relative safety of apartment block entrances as a siren sounded, a scene repeated in other Israeli towns near the Gaza Strip.
Live television showed a double-burst of smoke in the clear skies above Tel Aviv as a rocket was intercepted.
In a bold infiltration, four Palestinian gunmen from Gaza landed ashore near Zikim, where a kibbutz and an army base are located, just across the border from the enclave.
The Israeli military said its troops shot them dead.
The surge in violence along the Gaza border - the worst since an eight-day war in 2012 when Tel Aviv was also targeted - followed a chain of events that were triggered by the abduction of three Israeli youths in the occupied West Bank on June 12.
The Israeli youths were found dead, as was a Palestinian teen abducted in East Jerusalem last Wednesday in a suspected revenge murder for which six Israelis have been arrested.
Israeli police say three of those people have confessed to the murder.
Hamas, which has neither confirmed nor denied any role in the kidnapping of the Israeli youths, has threatened an "earthquake" against Israel.
The Jewish state says Hamas has launched 200 rockets, but a Palestinian source close to the militant group said it was ready to restore calm if Israel met conditions, including a prisoner release.
Setting out terms for a ceasefire, the source said Israel had to "stop all forms of aggression", recommit to a 2012 Egyptian-brokered truce and free prisoners it detained in the West Bank last month.
Washington has backed Israel's actions, while France, Germany and the United Nations urged restraint on both sides.
"We strongly condemn the continuing rocket fire inside of Israel and the deliberate targeting of civilians by terrorist organisations in Gaza," White House spokesman Josh Earnest said.
"No country can accept rocket fire aimed at civilians and we support Israel's right to defend itself against these vicious attacks."