Fighting has resumed between Israel and Hamas after talks in Egypt aimed at securing a longer-term ceasefire between the two collapsed.

Israeli officials say rockets were fired from Gaza, while Palestinian medics claim an Israeli airstrike has killed a toddler.

The two-year-old died when a house was struck in Gaza City, said Ashraf al Kidra, a spokesman for the local emergency services.

A 40-year-old woman and a third unidentified person were also killed in the blast, which came after Israel announced it had resumed airstrikes on Gaza after three rockets fired by Palestinian militants landed in open areas near the city of Beersheba.

Two of the dead are believed to be the wife and daughter of Gaza's military chief Mohammed Deif.

In a strike on the southern Gaza town of Deir el-Balah a pregnant woman, three children and two men were killed, emergency services said.

A further 21 people were injured in a separate airstrike that hit a building housing offices of Hamas's Al Asqa TV station.

Egypt talks collapse

The rocket fire from Gaza began several hours before a 24-hour extension of a five-day truce lapsed without renewal.

Israel condemned the attacks as a "grave and direct violation of the ceasefire".

There was no immediate claim of responsibility for the rocket attacks, including one in the Tel Aviv area, and no reports of any casualties.

But Hamas spokesman Fawzi Barhoum hinted of more rocket fire, saying: "If Netanyahu doesn't understand ... the language of politics in Cairo, we know how to make him understand."

Hamas's military wing later said it had fired 40 rockets into Israel, one of which was aimed at Ben Gurion Airport, near Tel Aviv.

It threatened to fire more rockets at the country's main airport on Wednesday, saying the group had "decided to respond to the Israeli aggression" by making the airport a "target of attack" for the day.

Ezzat al Rishq, a senior Hamas official, also warned: "Israel will not enjoy security so long as the Palestinian people do not, and it started it."

Several thousands of Palestinians fled their homes in Gaza with bags of clothing, pillows and mattresses to seek shelter with relatives or in UN schools.

Israel withdrew its team from the indirect talks in Cairo, while Hamas officials said the chances of a durable ceasefire were "evaporating" and blamed the "Zionist occupation" for the lack of progress in negotiations.

The US said it was concerned by the breakdown in talks and laid the blame squarely on the Palestinian militant group.

"Hamas has security responsibility for Gaza... Rocket fire came from Gaza," State Department spokeswoman Marie Harf said.