At least 20 people have been killed in a crush at an aid distribution centre in southern Gaza run by the US- and Israel-backed Gaza Humanitarian Foundation (GHF), the organisation and a local hospital say.

The GHF said 19 were trampled to death and one was stabbed “amid a chaotic and dangerous surge” at its site in the Khan Younis area. It added that it believed people “armed and affiliated with Hamas” fomented unrest.

But Gaza’s Hamas-run Government Media Office denied the claim and accused the GHF of trying to “cover up” a crime.

Nasser hospital in Khan Younis said it had received the bodies of 21 people who died from suffocation as a result of tear gas inhalation and a crush at the aid site.

It is the first time the GHF has confirmed deaths at one of its aid sites.

In a graphic video shared on social media and verified by the BBC, a witness standing on a cart filled with the bodies of six boys and men at Nasser hospital said they had been crushed between fences set up at the GHF site while waiting for food handouts on Wednesday.

“They are children. What is it their fault dying for aid?” the man shouts as he holds up the body of one of the boys.

“What happened is [that] at the door of the aid [site], the foreigners made a fence here and a fence here,” he gestured. “The boys went to the front and the people came and stepped on them.”

One injured man being treated at the hospital, Mahmoud Fojo, 21, said that when he reached the GHF site he found that contractors were “closing the gates”.

“People kept gathering and pressuring each other. When people pushed each other, those who couldn’t bear it fell down under the people and got run over,” he told Reuters news agency.

“Those who couldn’t stand fell under the people and were crushed. Some people started jumping over the wire fence and got wounded.”

Another man, Ahmed Abu Omra, said armed contractors standing near the narrow passageways into which the crowds were funnelled had fired “pepper bombs”.

The Government Media Office accused the security contractors of causing the crush by closing the gates of the site after thousands of people had gathered in narrow channels, and then firing canisters of tear gas and live rounds towards them.

A GHF spokesperson said the claim was “completely false”.

“At no point was tear gas deployed, nor were shots fired into the crowd. Limited use of pepper spray was deployed, only to safeguard additional loss of life.

“In at least one instance, an American worker physically entered the violent crowd to rescue a child who was being trampled,” they added.

The GHF uses private security contractors to distribute aid from sites in Israeli military zones. Israel and the US say the system is necessary to stop Hamas from stealing aid.

The UN refuses to co-operate with it, describing its set-up as unethical.

There have been almost daily reports of Palestinians being killed while seeking aid since the GHF began operations in late May. Witnesses say most have been shot by Israeli forces.

A spokesperson for the UN human rights office, Thameen Al-Kheetan, told the BBC that it was aware of the reports about Wednesday’s incident but did not have any details.

“In general, there is a severe shortage of humanitarian assistance and life-saving aid in Gaza. Hundreds of thousands of hungry people have to gather at only three or four distribution points managed by the Gaza Humanitarian Foundation,” he said.

“We continue to record reports of shootings or shelling by the Israeli military in the vicinity of these sites. Therefore, increasing desperation and breakdown of law and order are resulting in a high level of chaos.”

Kheetan called on Israel, as the occupying power, to “facilitate the full and unimpeded access to Gaza of humanitarian assistance commensurate with the needs of the civilian population”.

On Tuesday, the UN human rights office said it had so far recorded 674 killings in the vicinity of the GHF’s four sites in southern and central Gaza over the past six weeks. Another 201 killings had been recorded along routes of UN and other aid convoys, it added.

Before Wednesday, the GHF had denied that there had been any deadly incidents in close proximity to its sites and accused the UN of using “false and misleading” figures from Gaza’s Hamas-run health ministry.

The Israeli military said last week that it recognised there had been incidents in which civilians had been harmed and that it was working to minimise “possible friction between the population and the [Israeli] forces as much as possible”.