By Nidal al-Mughrabi and Jeffrey Heller
GAZA/JERUSALEM, July 8 (Reuters) - At least 16 people were killed in strikes across the Gaza Strip on Tuesday, Palestinian officials said, as Israel threatened a lengthy offensive against Islamist militants whose rocket fire reached as far as Tel Aviv.
Israelis ran for cover as sirens sounded in the business capital, in the deepest attack from Gaza since hostilities flared three weeks ago after the abduction and murder of three Israeli teenagers. Air raid sirens later sounded in Jerusalem.
The military said its Iron Dome interceptor shot down the rocket which the Islamic Jihad militant group said it had fired.
Explosions echoed across densely populated Gaza, shaking buildings and sending up plumes of smoke. In residential areas, children could be heard crying as ambulance sirens wailed.
At least 12 civilians, including five children, were among the 16 dead in Gaza, Palestinian officials said. On the Israeli side, medics said rocket impacts wounded at least two people.
"We will not tolerate rocket fire against our cities and townships, and therefore I ordered a significant broadening of IDF (Israel Defence Force) operations against the terrorists of Hamas and other terror groups in the Gaza Strip," Prime Minister Benjamin Netanyahu said in a statement.
He called on Israelis to rally together and "show resilience, because this operation could take time".
Israeli officials said a ground invasion of Gaza was possible, but not imminent, and urged citizens within 40 km (24 miles) of the enclave to stay close to bomb shelters.
In scenes repeated in many Israeli towns near the Gaza Strip, motorists in the southern port city of Ashdod scrambled from their cars and raced for the relative safety of apartment block entrances as an air raid siren sounded.
In a bold infiltration, five gunmen from Hamas landed on the shore near Zikim, where a kibbutz and an army base are located, just over the border from Gaza. Israel's army said it shot them dead.
U.S. CONDEMNS ROCKETS
Washington 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."
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 begun by the abduction of three Jewish seminary students in the occupied West Bank on June 12.
Blaming Hamas, which neither confirmed nor denied involvement in the kidnapping, Israel arrested hundreds of the group's activists in their search for the teenagers who were eventually found dead, as was a Palestinian teen abducted in East Jerusalem last Wednesday in a suspected revenge murder.
Palestinians have since launched more than 200 rockets from Gaza, Israel says.
Hamas has threatened an "earthquake" against Israel. But it offered on Tuesday to restore calm if Israel halted the Gaza offensive, recommitted to a 2012 Egyptian-brokered truce and freed prisoners it detained in the West Bank last month.
"The enemy must not think about enjoying security unless these terms are met," the Hamas armed wing spokesman said.
The Israeli military said on Tuesday that, to support regular forces, it had called up 1,000 reserve troops out of a pool of 40,000 approved on Tuesday by the security cabinet. Some 1,500 other reservists have already been mobilised.
One Israeli attack overnight destroyed the house of a Hamas member's family, killing six people inside, locals said. The Palestinian Interior Ministry said the family had received a telephone call from an Israeli officer telling them to leave.
Locals said people had been urged to congregate there as "human shields" to deter a second attack after it was targeted earlier.
Another strike killed a Hamas commander and three others travelling in a car together, a pro-Hamas website said, identifying the senior Hamas man as Mohammed Shaaban.
Netanyahu said Israel was trying to target combatants only, saying: "Hamas deliberately hides behind Palestinian civilians, so it bears responsibility when they are inadvertently harmed." (Writing by Jeffrey Heller; Additional reporting by Mark Felsenthal in Washington; Editing by Robin Pomeroy)