Thousands of Palestinians overran anewly established aid sitein southern Gaza on Tuesday that is part of a controversial new Israeli- and US-approved aid distribution mechanism that began on Tuesday after months of blockade. Videos from the distribution site in Tel al-Sultan, run by the Gaza Humanitarian Foundation (GHF), showed large crowds storming the facilities, tearing down some of the fencing and appearing to climb over barriers designed to control the flow of the crowd. "I arrived at a place surrounded by Americans and the army. I tried to get closer, but because of the crowd, I couldn't get anything," said Wafiq Qdeih. "The Israeli army was shooting in the air, and the Americans and their workers retreated, making it impossible to distribute aid to the people. They want order, but there will be no order because these are desperate people who want to eat and drink." Several residents trying to access the aid told CNN they were grateful for the food they received, but described walking long distances to reach the distribution center, hours-long lines and general confusion. "The place is very far, and we struggled until we arrived. I am tired and exhausted. How can they provide food for all these people? There are too many people here; security will not be able to control them all," Abu Ramzi said. A diplomatic official called the chaos at the site "a surprise to no one." An 11-week Israeliblockadeon humanitarian aid has pushed the enclave's population of more than 2 million Palestinians towards famine and into a deepeninghumanitarian crisis, with the first resumption of humanitarian aid trickling into the besieged enclave last week. The GHF acknowledged the pandemonium, saying "the GHF team fell back to allow a small number of Gazans to take aid safely and dissipate. This was done in accordance with GHF protocol to avoid casualties." A security source said American security contractors on the ground did not fire any shots and that operations would resume at the site on Wednesday. The Israel Defense Forces said their troops fired warning shots in the area outside the compound and that the situation was brought under control. They denied carrying out aerial fire toward the site. "It's a big failure that we warned against," said Amjad al-Shawa, director of Palestinian Non-Governmental Organizations Network. "If Israel believes that through this blockade and emboldening starvation, which violates humanitarian principles, that this distribution method would work, they are mistaken." GHF said it has distributed about 8,000 food boxes totaling 462,000 meals in Gaza so far. They say the flow of meals will increase each day, with a goal of delivering food to 1.2 million – 60% of Gaza's population – by the end of the week. The GHF claimed it began operating on Monday, but photos from the organization showed only a handful of people carrying boxes of aid, with pallets of boxes sitting at an otherwise empty lot. GHF is readying three additional sites for the distribution of aid, two of which are in southern Gaza and one in central Gaza. All of the sites in the south are in an area that fell under a massive evacuation order one day earlier. There are no distribution sites in northern Gaza – a point of criticism from many aid experts. The UN has previously warned that the fact the initial sites were only insouthern and central Gazacould be seen as encouraging Israel's publicly stated goal of forcing "the entire Gazan population" out of northern Gaza, as Defense Minister Israel Katz put it earlier this month. "This mechanism appears practically unfeasible, incompatible with humanitarian principles and will create serious insecurity risks, all while failing to meet Israel's obligations under international law," the UN Office for the Coordination of Humanitarian Affairs wrote earlier this month in a document obtained by CNN. In a briefing with reporters on Tuesday an Israeli military official said that both the new mechanism and the old mechanism under the United Nations are working now. The Coordinator of Government Activities in the Territories (COGAT) said 95 trucks entered Gaza on Tuesday. The UN Relief and Works Agency for Palestine Refugees (UNRWA) had earlier said that it is ready, with other humanitarian organizations, "to distribute meaningful quantities of aid the moment we are allowed to" but that the amount of families permitted into Gaza so far have been "minimal." Jens Laerke, a spokesperson for the UN aid coordination office, has criticized the GHF aid plan as "a distraction from what is actually needed, which is a reopening of all the crossings into Gaza, a secure environment within Gaza and faster facilitation of permissions and final approvals of all the emergency supplies that we have just outside the border." Israel and the US had declined to name the humanitarian organizations involved in the controversial new mechanism, but images from the GHF showed boxes labeled "Rahma Worldwide," a Michigan-based non-profit organization that says it provides "aid and assistance to the most vulnerable communities in the world." This story has been updated. Dana Karni contributed to this report. For more CNN news and newsletters create an account atCNN.com