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 Médecins Sans Frontières (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.

Rwandan refugees flee the fighting in 1994 Rwandan refugees flee the fighting in 1994. Photograph: Pascal Guyot/AFP

“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.

More: Mission Congo: How Pat Robertson Raised Millions on the Back of a Non-Existent Aid Project