Israel launched air strikes on Gaza on Friday morning after Islamist groups there refused to extend a ceasefire and resumed rocket fire.

At least 35 rockets were fired from Gaza towards Israel after a 72-hour ceasefire expired at 8am local time. Several more had been fired during the night.

By noon there were reports of air strikes in the north and east of Gaza and several audible explosions in Gaza City. There appear to have been some casualties, though details were unclear.

There were also reports of injuries in Israel from rocket strikes. At least one rocket appeared to have fallen short, landing in Gaza.

The Hamas spokesman Fawzi Barhum told the AFP news agency: "All the Palestinian factions, including Hamas, have agreed not to renew the ceasefire because [Israel] is refusing to accommodate our demands."

An Israeli official said the prime minister, Binyamin Netanyahu, had ordered the military to "retaliate forcefully to the Hamas breach of the ceasefire". The Israeli army said it had targeted "terror sites" across the Gaza Strip, and no Israeli soldiers had entered the Palestinian territory.

It is unclear whether Hamas or other smaller factions in Gaza, such as Islamic Jihad, fired the rockets at Israel.

In Gaza, tens of thousands of people who had returned to their homes during the 72-hour ceasefire rushed back to the UN-run shelters where many have been staying since the war began more than four weeks ago.

At one school, 800 people who had left in recent days returned on Friday morning as news of the renewed fighting broke. One was Nidal Sultan, 21, who had driven with six members of his family from the northern town of Beit Lahiya.

"We were in the school on the first day of the ceasefire and came back this morning," he said. "There were strikes and shelling in the last hour or so. It's not safe, so we have to come to the school however bad it is. We will stay now until the war stops."

UN worker Amal Zaqqout said the school was now holding more displaced people than before the ceasefire. "We are very, very crowded. We have 2,000 or more people living in corridors, in classrooms, everywhere. Thank God we have not had any transmissible diseases, but that is definitely a concern now," Zaqqout said.

Before the ceasefire, more than a quarter of Gaza's population of 1.8 million had been displaced. About half were in UN shelters, and many of the rest stayed with relatives. About 65,000 are believed now to be homeless.

Most people in Gaza blamed Israel for the renewal of hostilities and said they supported the demands made by the Palestinian delegation in Cairo during indirect negotiations brokered by the Egyptians in recent days. Chief among those demands has been the lifting of the eight-year blockade of Gaza by Israel and Egypt.

"The people's demands are humanitarian. Even if the resistance agreed to drop the demands, the people would not agree. We are at the point where life or death is the same thing for us," said Mohamed Eid, 40, who has been living in the grounds of the main hospital in Gaza since his house was destroyed in fierce fighting in the east of the city 15 days ago.

But Faiza Abu Khalil, 37, said she was "very worried and very scared" and still hoped for peace. Abu Khalil had returned to Gaza from her home near Beit Lahiya on Thursday night when it appeared the ceasefire would not hold.

A representative of the Mujahideen Faction, a minor group in Gaza, told the Guardian that further "sacrifices" by the Palestinian people would lead to the end of the blockade. "The people of Gaza are not willing to live under siege," he said.

More than 1,800 Palestinians have been killed and nearly 10,000 injured, the majority civilians, in the latest of three wars fought between Hamas and Israel since 2008. Three civilians have been killed by rocket fire from Gaza into Israel, and 64 Israeli soldiers were killed during ground operations that ended six days ago.

The ceasefire, declared on Monday night, had brought a palpable sense of relief and optimism to Gaza, but on Friday streets were deserted once more and any shops that had opened were hastily bring down their shutters.

Hamas officials in Gaza had threatened to restart hostilities if their demands were not met in the indirect negotiations with Israel that have continued in Cairo for most of the week.

The Palestinian delegation in Cairo has demanded that the Israeli-Egyptian blockade of Gaza is lifted and about 100 prisoners held by Israel are freed to secure a further truce. Israel insists Hamas must disarm, which officials from the Palestinian group said on Thursday was "inconceivable".

More than 3,000 rockets have been fired from Gaza into Israel in recent weeks. Most of those headed for inhabited areas were shot down. A surge in rocket fire from Gaza prompted Israel to launch air strikes almost a month ago.

Statements by Hamas officials in Gaza were echoed by members of the Palestinian negotiating team in Cairo on Thursday. "If the Israelis don't agree, we will go back and fight through the tunnels," one said.

The discovery of dozens of tunnels between Gaza and Israel, which could be used to mount attacks to kill or kidnap civilians and soldiers, was cited as the main reason Israel sent ground forces into Gaza after days of aerial bombardment last month.

The destruction of the tunnels discovered by Israeli troops was also given as the reason for ending the ground operation. The new threat, however, suggests further tunnels may exist.