Museum curators are warning of a mysterious man posing as a Jesuit priest who is suspected of duping American institutions with brilliantly forged artworks over the past 20 years.

A picture is emerging of one of the most bizarre cases of deception in art history. Unlike other forgers, the "priest" does not ask for payment of any kind for his Picassos, Signacs and Daumiers which have been described as "masterful". It seems the alleged fraudster simply enjoys fooling museum experts who have not only accepted his fakes as cherished gifts but invited him to "special donor events" in the belief that he has more to give.

Research by senior museum figures suggests he has targeted more than 30 museums so far and institutions across the United States are now being warned to look out for him. Whether he has visited British museums bearing gifts is unclear.

As the priest, he explains that he wants to give a work of art in memory of his late mother who came from wherever the museum is located. He tells them that, as a minister, he cannot keep it for himself.

He is also suspected of acting under two other aliases. Sometimes his story involves a donation in memory of his late father, whom he describes as having been a high-ranking military officer. Ceremoniously handing over his work to the grateful institution, he hints at other possible donations before making his exit.

A dossier on the forger has been produced by Matthew Leininger, director of museum services at the Cincinnati Art Museum. The unpublished report, seen by the Guardian, notes: "[The forger] pays his own air fare and hotels when travelling, but gets wined and dined by the institutions because he has told everyone that he has many more works in his collection and promises more work plus money. He also claims to have bad health and heart problems … 'I'll be back in touch for further gifts after I recover from heart surgery'. He is treated as royalty because people have believed they are getting great works and money." Mr Leininger is now alerting the museum world to the deception.

One theory is that, like many forgers, this one is embittered by his struggles to find recognition under his own name. His fakes are described as so perfect that most cannot be detected without high magnification. In addition, their "authenticity" is boosted by fake documents, including auction house catalogue entries.

Leininger believes the "donations" go back to at least 1987. He first encountered the forger while working at the Oklahoma City Museum of Art, which was offered a watercolour boating scene by "Paul Signac". According to the dossier, research eventually unmasked it as a fake, along with another "Signac" at the Memphis Brooks Museum of Art. A genuine Signac from which the latter forgery was copied is in the Hermitage in St Petersburg.

Most recently, the forger donated a work to the Hilliard University Art Museum at the University of Louisiana. When the museum's director, Mark Tullos Jr, looked more closely at the painting, supposedly by the American impressionist Charles Courtney Curran, doubts were raised. Scrutiny under a black light revealed telltale signs of bleach found in most contemporary papers and linens.

Tullos is also circulating warnings: "We were contacted by a man posing as a Jesuit priest … we have reported him to the federal authorities."

Asked how the forger had been able to continue operating for so long, Tullos said institutions that accepted the works into their collections were "a little bit embarrassed to disclose that this happened".

Commenting on whether there were likely to be many forgeries on museum walls, he added: "There have got to be more out there."