Aid shipments into southern Gaza are being squeezed out by commercial convoys, humanitarian organisations say, at a time when Israel’s military push into Rafah has choked off supply routes critical to feeding hundreds of thousands of people.

Deliveries of food, medicine and other aid into Gaza fell by two-thirds after Israel began its ground operation on 7 May, UN figures show. But overall the number of trucks entering Gaza rose in May compared with April, according to Israeli officials.

Part of the reason for the stark difference in accounts of what supplies reached the strip is a rise in commercial shipments.

In May, the Israeli military lifted a ban on the sale of food to Gaza from Israel and the occupied West Bank, Reuters reported last week. Traders got the green light to resume buying fresh fruit and vegetables, dairy and other goods.

Inside Gaza, residents say there is more food in markets, but prices are many times higher than prewar levels, and after months of fighting and displacement few people can afford to buy much.

A group of aid agencies warned this week that there was a “mirage of improved access”, when efforts to feed Palestinians were on the verge of collapse.

“While Kerem Shalom remains officially open, commercial trucks have been prioritised, and the movement of aid remains unpredictable, inconsistent and critically low,” a group of 20 aid agencies warned this week.

In April, about 5,000 truckloads of aid came through Kerem Shalom and Rafah, the two main crossings into southern Gaza, UN data shows. In the last three weeks of May, just a few hundred came through Kerem Shalom; Rafah has been closed.

Overall, however, Israel says the average daily number of trucks going into Gaza rose in May to about 350, from about 300 in April, and the “vast majority” of recent deliveries passed through Kerem Shalom, said Shimon Freedman, spokesperson for Cogat, the Israeli body responsible for humanitarian coordination. There was no priority for commercial shipments, he added.

Ami Shaked, the manager of the crossing complex where shipments are checked by Israeli security, confirmed that truck deliveries for business were outpacing aid, but said it was driven by the commercial interests of logistics firms.

“This problem is the same on two sides (of the crossing), the Palestinian sides choose to take the goods of the businessmen … the Israelis the same,” he told journalists at Kerem Shalom.

“Because if I have a contract with UNWRA [the UN agency for Palestinian refugees], they will pay, for example, 2,000 shekels for each truck. The market now (for) pure business is between 7,000 and 10,000 for each truck, so they prefer to take the goods of the businessmen.”

Aid organisations dispute that, saying they have long-term contracts for trucks, and when limited capacity to enter Gaza and move through a military zone is allotted to commercial trucks, it exacts a toll on the ability to ship in aid supplies.

Obstacles include lack of permits from Israeli troops to drive to Kerem Shalom, and roads into the collection area that are snarled by commercial vehicles waiting to load and unload.

“The Israeli military operation and activities since 6 May have been crippling to the humanitarian response,” said Juliette Touma, communications director for UNWRA.

“(The reasons) include restrictions imposed on our movement, including to pick up humanitarian supplies from Kerem Shalom. The Israeli authorities have not been giving us enough authorisations to move …. Also the area around Kerem Shalom has very, very quickly become extremely dangerous.”

Aid workers have long called for more trade into Gaza, to complement the supplies they can deliver. Food for sale allows those who can afford it to have a healthier, more varied diet, and potentially take some pressure off the demand for aid.

But if bringing more food to markets comes at the cost of aid deliveries, it will deepen rather than relieve the hunger crisis that is escalating in southern Gaza. Last week, two child deaths from malnutrition were reported in Deir al Balah hospitals.

“For the largest period in the war, Israeli authorities were almost exclusively allowing humanitarian supplies, although not enough of them. This made a whole population of 2 million people rely on humanitarian handouts and relief,” Touma said.

“Then they started bringing in commercial supplies, once people had depleted their resources, and there’s a huge issue of cash shortages in Gaza. Very, very few people will be able to afford those supplies that are coming in.”

After months of war, many Palestinians are running out of money, and almost all have trouble accessing cash. Most have been out of work for months, and those still getting salaries or with savings in the banks cannot use card or electronic payments, because power and communications networks barely function.

The very few ATMs that are still functioning have queues many hours long, a low cap on how much can be withdrawn, and a percentage must be paid to protection groups that prevent theft and rioting at the cash machines.