* Hamas unleashes dozens of rockets at Israel after deadly strike
* Gazan child, woman die in explosion
* Truce talks collapse; Israel recalls negotiators from Cairo (Adds Gaza death toll, 3, intense rocket fire at Israel)
By Nidal al-Mughrabi and Jeffrey Heller
GAZA/JERUSALEM, Aug 19 (Reuters) - A ceasefire in the Gaza Strip collapsed on Tuesday, with Palestinian militants firing dozens of rockets at Israel and Israel launching air strikes that health officials said killed three people including a woman and a young girl in Gaza.
Accusing Gaza Islamists of breaking the truce, Israel promptly recalled its negotiators from talks in Cairo, leaving the fate of Egyptian-brokered efforts to secure a lasting peace hanging in the balance.
Rockets were fired from Gaza nearly eight hours before a ceasefire - extended by a day on Monday - was due to expire. Later dozens of rockets took aim at a number of cities and one missile hit open land in the greater Tel Aviv area, causing some damage but no casualties.
Gaza witnesses said Israeli aircraft launched 35 attacks, including one on a house in Gaza City, where hospital officials said a woman and a two-year-old girl were killed. A third unidentified person also died in the strike, officials said.
Israeli media said Israel had targeted a senior Hamas figure at the house that was bombed, possibly the head of a rocket launching operation. The army declined to comment on the bombing of that particular home in Gaza City, saying only that it had bombed 30 sites across Gaza on Tuesday.
Gaza's dominant Islamist group Hamas said it fired at least 40 rockets at Israel after that deadly hit, targeting Jerusalem and the Tel Aviv area including Israel's Ben-Gurion International Airport. An Israeli security official said there was no disruption of activity at the airport.
A police spokesman said a car was damaged in Tel Aviv and a rocket was intercepted in the Jerusalem area, where witnesses heard several explosions shortly after warning sirens sounded, and the military said one rocket struck inside an open area.
"Police have stepped up patrols in response to the wave of rocket fire," spokesman Micky Rosenfeld said.
Hamas's armed wing issued a statement after the rocket barrage accusing Israel of "violating the calm and committing a massacre ... the enemy has opened the gateway to hell." It vowed Israel would "pay a heavy price" for its air strikes.
Earlier Hamas had denied any involvement in rocket fire when three rockets struck in the Beersheba region in southern Israel, which Israel denounced as a violation of a truce eight hours before it expired at 2100 GMT or midnight local time.
Mark Regev, a spokesman for Prime Minister Benjamin Netanyahu, called that initial attack "a grave and direct violation of the ceasefire" and a military spokesman said that in response to the salvoes, "terror targets across the Gaza Strip" were attacked.
On Netanyahu's order, Israeli delegates to the indirect talks in Cairo on ending the Gaza war and charting the territory's future, immediately flew home.
Israel has said repeatedly that it will not negotiate under fire, and Egyptian mediators have been struggling to end the five-week-old Gaza conflict and seal a deal that would open the way for reconstruction aid to flow into the territory of 1.8 million people, where thousands of homes have been destroyed.
The Palestinian Health Ministry says some 2,019 people, mostly civilians, have been killed in the small, densely populated coastal territory since fighting started on July 8.
Sixty-four Israeli soldiers and three civilians in Israel have also been killed during the offensive, which the Jewish state launched with the stated aim of halting militant fire.
MORE VIOLENCE FEARED
Suggesting that Israel expected more violence, the military instructed Israeli civilians to open bomb shelters as far as 80 km (50 miles) from Gaza, or beyond the Tel Aviv area.
Israel's Channel 10 TV said those instructions may have been issued in anticipation of the retaliation that might follow were Israel to target a senior Hamas official. The station did not identify the official.
Israelis living within a seven km (four mile) range were urged to sleep in safe rooms or shelters.
Israeli media said municipalities in the Tel Aviv area were reopening shelters they had shut when fighting subsided two weeks ago.
The violence also prompted a new exodus of dozens of Palestinian families who had fled previous fighting and had returned home only days ago.
A Palestinian delegate in Cairo said negotiations for a durable ceasefire were near collapse. "The talks have been suspended unofficially," said Qais Abdel Karim of the Popular Front for the Liberation of Palestine.
The Palestinians want Egypt and Israel to lift their blockades of the economically crippled Gaza Strip that predated the Israeli offensive.
Hamas leader Izzat al-Risheq told reporters at a Cairo hotel he believed chances of reaching another truce were "very weak". Risheq posted on Twitter that Egypt was awaiting an Israeli response before the truce officially expired.
Israel, like Egypt, views Hamas as a security threat and wants guarantees that any removal of border restrictions will not result in militant groups obtaining weapons.
A senior Palestinian official in Gaza said sticking points to an agreement in the Cairo talks have been Hamas's demands to build a seaport and an airport, which Israel wants to discuss only at a later stage.
Israel has called for the disarming of militant groups in the enclave. Hamas has said that laying down its weapons is not an option.
Punctuated by several temporary ceasefires, the scale of fighting had diminished greatly since Israel pulled its ground troops out of Gaza two weeks ago and it had seemed there was little appetite on either side for the war to drag on.
However, Netanyahu said on Monday the Israeli military was prepared to take "very aggressive action" if shooting against Israel resumed.
Israel and Hamas have not met face-to-face in Cairo, where the talks are being held in a branch of the intelligence agency, with Egyptian mediators shuttling between the parties in separate rooms. Israel regards Hamas, which advocates its destruction, as a terrorist group. (Additional reporting by Allyn Fisher-Ilan and Maayan Lubell in Jerusalem and Stephen Kalin in Cairo; Writing by Jeffrey Heller, Editing by Ralph Boulton, Crispian Balmer and Howard Goller)