One of the stranger sights of the refugee crisis that followed the 1994 Rwandan genocide was of stretcher-bearers rushing the dying to medical tents, with men running alongside reciting Bible verses to the withering patients.

The bulk of the thousands of doctors and nurses struggling to save lives – as about 40,000 people died of cholera – were volunteers for the international medical charity MÃ©decins Sans FrontiÃ¨res (MSF). The Bible readers were hired by the American televangelist and former religious right presidential candidate, Pat Robertson, and his aid organisation, Operation Blessing International.

But on Robertson's US television station, the Christian Broadcasting Network, that reality was reversed, as he raised millions of dollars from loyal followers by claiming Operation Blessing was at the forefront of the international response to the biggest refugee crisis of the decade. It's a claim he continues to make, even though an official investigation into Robertson's operation in Virginia accused him of "fraudulent and deceptive" claims when he was running an almost non-existent aid operation.

"We brought the largest contingent of medicine into Goma in Zaire, at least the first and the largest," Robertson said as recently as last year on his TV station.

Now a new documentary lays bare the extent of the misrepresentations of Operation Blessing's activities in the Democratic Republic of Congo, formerly Zaire, that it says continue to this day.

Mission Congo, by David Turner and Lara Zizic, opens at the Toronto film festival on Friday. It describes how claims about the scale of aid to Rwandan refugees were among a number of exaggerated or false assertions about the activities of Operation Blessing which pulls in hundreds of millions of dollars a year in donations, much of it through Robertson's televangelism. They include characterising a failed large-scale farming project as a huge success, and claims about providing schools and other infrastructure.

But some of the most damaging criticism of Robertson comes from former aid workers at Operation Blessing, who describe how mercy flights to save refugees were diverted hundreds of miles from the crisis to deliver equipment to a diamond mining concession run by the televangelist.

Throughout the Rwandan refugee crisis, when more than 1 million people fled into neighbouring Zaire and started dying en masse of cholera, Robertson told his viewers that Operation Blessing was at the forefront of saving lives.

"It was the most important first medical shipment on the scene out of everything," he said of one aid delivery as he appealed for donations.

In another broadcast, Robertson said Operation Blessing was saving thousands of lives.

"The death toll in this particular camp went down to almost zero because of our people being there," he said.

Robertson claimed that Operation Blessing sent plane-loads of doctors.

"These are tents set up with our doctors and our medical teams that came from here to work as hard as they could to save lives," Robertson said over pictures of a large tent of children on drips being tended by nurses and doctors.

But the film was of MSF medical staff at work. Operation Blessing had just one tent and a total of seven doctors. MSF officials who worked in Goma told the documentary-makers that they had no recollection of even seeing Operation Blessing – let alone working with it.

"What's really unacceptable is that Operation Blessing took photographs of MSF workers and then used this in their fundraising," said Samantha Bolton, the former MSF spokeswoman in Goma.

Officials from other aid operations said that Operation Blessing was not anywhere near the first or largest groups working in Goma. Jessie Potts, the operations manager for Robertson in Goma in 1994, told Mission Congo that the medicines that did arrive were not of great use in fighting the cholera epidemic.

"We got a lot of Tylenol. Too much. I never did understand that. We got enough Tylenol to supply all of Zaire. God, I never saw as much in my life," he said.

Then, Potts said, suddenly everything changed. "Operation Blessing, several weeks into the operation, decided not to send any more medical teams," he said. The flights to Goma dried up.

Robert Hinkle, the chief pilot for Operation Blessing in Zaire in 1994, said he received new orders. "They began asking me: can we haul a thousand-pound dredge over? I didn't know what the dredging deal was about," he said.

The documentary describes how dredges, used to suck up diamonds from river beds, were delivered hundreds of miles from the crisis in Goma to a private commercial firm, African Development Company, registered in Bermuda and wholly owned by Robertson. ADC held a mining concession near the town of Kamonia on the far side of the country.

"Mission after mission was always just getting eight-inch dredgers, six-inch dredgers … and food supplies, quads, jeeps, out to the diamond dredging operation outside of Kamonia," Hinkle told the film-makers.

The pilot said he joined Operation Blessing to help people. Of the 40 flights he flew into Congo, just two delivered aid. The others were associated with the diamond mining. "We're not doing anything for those people," he said. "After several months I was embarrassed to have Operation Blessing on the airplane's tail." He had the lettering removed.

Robertson ordered an airstrip carved out of the bush next to the town of Kamonia, 800 miles from Goma. On his television show he left the impression this was part of his aid operation.

The televangelist was also raising donations for Operation Blessing's other activities in Congo. These included a 100,000-acre farm near the town of Dumi, which Robertson claimed had produced a large harvest of corn and was a "tremendous feeding station".

"The soil is unbelievable. You stick anything in the ground and it grows. You put a shovel in and it starts sprouting," he said in appealing for donations.

In fact, the farm at Dumi had already failed. The soil was of poor quality and Operation Blessing brought seeds from the US unsuited to the region.

To this day, Robertson continues to solicit donations on the back of the project, on the grounds that although the farm failed, it left a legacy with a school that established a "foundation of education" in the town. 2011 posting on the Operation Blessing website described the school as "thriving".

"Despite the turbulence over the years, the children of Dumi still gather to learn and grow in the little school house on the plateau," it said.

Yet Mission Congo visited the Dumi school at the same time and filmed it abandoned, stripped of its desks and falling down.

Similarly, local leaders in Kamonia said that they were promised schools, roads and a hospital by Robertson's mining company – but none of it materialised.

Robertson's activities in Congo were initially exposed by a Virginia newspaper, the Virginian Pilot, in the 1990s. The investigation by Bill Sizemore prompted the attorney general in Virginia, where Operation Blessing is registered, to order a probe by the state's office of consumer affairs.

Its report concluded that Robertson made "fraudulent and deceptive" statements with claims to be ferrying doctors and medical aid to Goma when he was delivering diamond-mining equipment. It accused Operation Blessing of "misrepresenting" what its flights were doing, and of saying that the airstrip at Kamonia was part of the aid operation when it was "for the benefit of ADC's mining operation".

It also said Robertson had falsely portrayed the Dumi farm as hugely successful when it had already failed.

"Pat Robertson made material claims, via television appeals, regarding the relief efforts. These statements are refuted by the evidence in this case," the report said.

But the Virginian authorities declined to prosecute Robertson, describing his misrepresentations as a "blemish". Mission Congo notes that leading state politicians were recipients of large donations from Robertson.

Robertson has been embroiled in mining controversies elsewhere in Africa. He supported the then president of Liberia, Charles Taylor, during that country's civil war without revealing at the time that he had an $8m investment in a Liberian gold mine. Taylor was already indicted by a UN war crimes tribunal at the time and was later convicted of crimes against humanity.

Robertson has consistently denied the accusation of misusing donations and claimed that the Virginia authorities' failure to prosecute effectively cleared him of wrongdoing. He has acknowledged the diamond mining operation but said that it was small scale and produced few gems.