Pure evil is all around in this unnervingly subtle, sophisticated movie; an eerie oppression in the air. Andreas Fontana is a Swiss director making his feature debut with this conspiracy drama-thriller, shot with a kind of desiccated blankness, about the occult world of super-wealth and things not to be talked about. The title is a Swiss banker’s code-word in conversation for “Be silent”.

It is set in 1980 in Argentina, at the time of the junta’s dirty war against leftists and dissidents, and you could set it alongside recent movies including Benjamín Naishtat’s Rojo (2018) and Francisco Márquez’s A Common Crime (2020), which intuited the almost supernatural fear among those left behind when people they knew had vanished and joined los desaparecidos, the disappeared ones. But Azor gives a queasy new perspective on the horror of those times, and there is even a nauseous echo of the Swiss banks’ attitude to their German neighbours in the second world war.

Yvan (Fabrizio Rongione) is a private banker from Geneva – elegant, discreet, an excellent speaker of Spanish, English and French – who is making what appears to be an emergency diplomatic visit to soothe his well-heeled and secretive clients in Argentina. He is doing so with his elegant, supportive wife Inés (Stéphanie Cléau); her presence there is also intended to be emollient, to signal that nothing is seriously wrong, and that this is almost by way of a social call. Yvan’s clientele are deeply troubled by the new political regime, and it is not simply because one has a grownup daughter with liberal views who has unaccountably gone missing. The super-rich fear that they could find their assets being sequestrated by the government. One of them talks of thoroughbred racehorses being “disappeared”. And what is even worse is that these people were used to dealing with Yvan’s colleague Réné, a genial and exuberant figure who has also now vanished.

Yvan is utterly at a loss as to how or why Réné could have disappeared … but he has done so in Buenos Aires. Strangely, Réné kept an apartment in the city, and appears to have recently, in some oddly colonial way, “gone native”. Yvan searches through this now deserted flat, finding only a list of familiar client names and one more word: “Lazaro”. And in the final, chilling sequence involving a Conradian trip downriver, this word appears to refer to a new secret government contract or income-generating scheme, a way of reviving money from the dead: the sort of thing a Swiss bank could help with. Could it be that Réné was disappeared because he broke the azor code and told people about Lazaro? Or even invented Lazaro himself?

Part of the chill in Azor is the professional calm cultivated by Yvan and Inés; Yvan affects never to be really upset or distressed about what has happened to Réné and what is happening all around him. When the couple arrive in the city, their car is held up at a roadblock caused by the military police arresting two young men at gunpoint. Fontana’s camera shows these two at a distance across the street with their hands up and then, in the next shot, there is only one of them. Yvan and Inés look away.

With bizarre obtuseness, Yvan is upset about losing clients for being too conservative, too sober. A boorish racehorse-owner and his obnoxious lawyer tell Yvan they are taking their business elsewhere. An elderly monsignor is impatient with cautious Yvan, who does not want to get involved in the risky, vulgar world of currency trading. But all of his conversations take place in an air of studied politeness. The fact that Yvan comes from Geneva meets with everyone’s approval because it was the favourite city of Jorge Luis Borges; the city that always stays the same. These people love private clubs, gentlemen-only boxes at the races or, in more relaxed form, hanging out by private pools. (It’s a little like the way the swimming pool was an emblem of torpor and stagnancy in Lucrecia Martel’s 2001 film La Cienaga, or The Swamp.)

There is something dreamlike in the series of social calls that Yvan and Inés make to a succession of wealthy, elderly, melancholy people who sense that their lives and their prosperity are coming to an end but never respond to any sense of emergency. It is a film that continues to echo mysteriously inside my head.

• Azor screens at the London film festival and is released in the UK on 29 October.