With Egypt having all but shuttered its border with Gaza, Israel allowed about twice the number of Gazans to exit through its Erez crossing in the first half of 2015 as in the same period the year before. But the permits are reserved mainly for merchants and medical patients, and some Gazan doctors and residents, as well as officials involved in the issuing of permits, say they have seen a parallel uptick in fraudulent referrals, slowing approvals for legitimate cases.

There is no firm data on how prevalent the practice is. The World Health Organization reported that 2,148 Gaza patients applied for permits in June, the highest monthly number since the agency began monitoring the process in 2006; 80 percent got through, a drop from the previous three months. The nonprofit Physicians for Human Rights wrote to the Israeli authorities last week complaining that eight patients who it had helped apply for medical transfers were denied permits in August, up from a typical two per month.

“We have a lot of cases of both fake papers and fake requests, and also just people that don’t really need to get this treatment outside,” said the Israeli official who heads the permit division, speaking on the condition of anonymity because of his sensitive role. “Sometimes we find ourselves digging deep in certain requests just to make sure they’re real, and other real requests are waiting.”

Patient applications from Gaza nearly quadrupled in less than a decade, to more than 18,000 in 2014 from 5,470 in 2006; there were 10,034 requests in the first half of 2015. Dr. Bassem al-Badri, a Palestinian dermatologist who runs Gaza’s medical-referral office, and Anita Vitullo, manager of the W.H.O.’s health-advocacy project for Palestinians, both said the main drivers are Gaza’s swelling population and the shortage of medicine, equipment and personnel in its overburdened hospitals, especially since last summer’s war with Israel.

But Dr. Badri said that “about 10 percent” of applicants did not actually need treatment and that there were doctors in Gaza who charged patients $200 to $2,000 for unnecessary referrals. He blamed Israel for the growing black market, calling it “one of the crimes of the occupation.”