Israel’s defence minister has rejected United Nations and European Union calls for an investigation into the killing of more than a dozen Palestinians by the military during demonstrations on the Gaza frontier.

Gaza’s coastal enclave has been shaken by the bloodiest episode in years after protests advertised as peaceful sit-ins turned violent, with Israeli troops firing rounds of live ammunition at crowds of stone-throwers.

Hospitals in Gaza have recorded hundreds of emergency admissions from the protest, and doctors have said most were for gunshot wounds.

The UN secretary general, António Guterres, and the EU’s top diplomat, Federica Mogherini, called for independent inquiries into the bloodshed, which left 16 people dead.

But the Israeli defence minister, Avigdor Lieberman, told Israel’s public radio on Sunday that there will not be an inquiry. “From the standpoint of the [Israeli Defence Force] soldiers, they did what had to be done,” he said. “I think that all of our troops deserve a commendation.”

Q&A What is the history of the Palestinian reconciliation efforts? Show The two main Palestinian parties – the Fatah faction of Palestinian Authority president Mahmoud Abbas and the Islamist militant group Hamas – have run separate governments in the West Bank and Gaza respectively since 2007. The situation emerged after Hamas defeated Fatah in parliamentary elections in 2006. Fatah refused to recognise the result, leading to a near-civil war that saw Hamas push Fatah out of Gaza. Numerous attempts at reconciliation have ensued but the latest effort looks the most serious yet. The issue of who controls the borders and runs government ministries is a key test, not least in loosening the Israeli blockade on Gaza, imposed after Hamas took control.

Responsibility for land border crossings – in a coastal strip without a commercial sea port or airport – is crucial, as Palestinians and goods can only cross by these checkpoints. Both Egypt and Israel will want to ensure that no arms reach Hamas and other groups.

Israel has accused Gaza’s rulers, Hamas, of using “violent riots to camouflage terror”. It also pointed to an attempted gun attack on Friday against soldiers along the border.

Israeli army spokespeople have said claims by the Gaza health ministry that more than 750 people were wounded by live fire are exaggerated.

At the Gaza Strip’s main Shifa hospital, the digital registry of A&E admissions on Friday, seen by the Guardian, showed that from 8.45am until the end of the day, 275 people from the protest arrived. It did not specify injuries, but doctors said most had gunshot wounds to the legs.

A clerk said a further eight patients were transferred from surrounding clinics to Shifa’s operating theatres. Surgeons said many patients had large exit wounds.

On Sunday a 23-year-old man, Adam Abu Ghanima, said he had just driven to the hospital from a demonstration, which was smaller than Friday’s. His kneecap had been pierced and blood soaked the sheets of the bed where he lay.

He said he had planned to place a Palestinian flag near the frontier. “I was right next to the Israeli soldiers. Before they shot me, they fired warning shots in the air,” he said. But he kept going, he added, “to bring Jerusalem back”.

Another man said he had been shot trying to lift a Palestinian flag that had fallen over on the Gazan side.

Doctors said most of those admitted since Friday had been discharged, but some awaiting surgery lay in beds surrounded by friends and families.

Ibrahim Fathi Hasna, 22, said he and another man who had wire cutters and a Molotov cocktail had managed to cut through a fence at a protest on Saturday to breach an Israeli-controlled area. They were both shot.

Hasna said he crawled back, eyes filled with teargas, until he was hoisted into an ambulance. The other man was hit in the back, he said, and he was unsure of his condition. Asked why he had wanted to cross the fence, he replied: “I just wanted to be there.”

The Great March of Return is a planned six-week demonstration calling for refugees and their descendants to be allowed back to their family homes in Israel. Backed by Hamas and other militant and political Palestinian factions, larger gatherings are expected every Friday, the holy day for Muslims.

Israel did not specify exact orders to troops, but a spokesperson said anyone approaching the “hostile border” was a potential threat. “People coming towards the fence, attempting to penetrate and break into the fence, damaging the infrastructure or using that area as a staging ground could potentially be shot,” said Lt Col Peter Lerner, of the Israel Defense Forces.

On Sunday Turkey’s president, Recep Tayyip Erdoğan, called Israel’s prime minister, Benjamin Netanyahu, a “terrorist”. Netanyahu tweeted that the Israeli army “will not be lectured by those who have indiscriminately bombed civilian populations for years”, referring to Turkey.

Gaza has been blockaded for a decade by Israel and Egypt, which tightly control goods and people entering the 140 sq mile area.

The demonstrations in Gaza appeared to be split in two, with women and children staying hundreds of metres from the perimeter fence, protesting in a festival-like atmosphere. Groups of mostly young men headed closer to throw rocks and light bottles of petrol. There have been no reports of Israeli casualties.

Israel said 10 of the dead belonged to Hamas. Hamas said five members of its armed wing who participated in the protest were killed.