Festival organiser Yury Samodurov said he was informed late on Tuesday by the cinema, the popular Kinocentre in central Moscow, that it would not host the free festival, already presented in Washington, New York and London, as previously agreed.
"My feeling is that the Kinocentre has come under pressure from the FSB," the Russian intelligence services, he told a press conference in Moscow on Wednesday.
Samodurov read out a letter from Kinocentre manager Vladimir Medvedev saying the screenings had been cancelled because "several of the foreign films were unacceptable for the Kinocentre."
Speaking on Moscow Echo radio, Medvedev said the non-Russian films "showed anti-Russian tendencies."
Moreover the films were "pure politics, and we are apolitical. There was no pressure on us, we simply don't show political films," he said.
But members of the festival organising committee were in no doubt where the responsibility for the cancellation lay.
"This is absolutely a political decision," said Anna Politkovskaya, the campaigning journalist who earlier in September presented the films in Britain and the United States.
"I thought this would be impossible. I'm shocked," she said. "For me the whole point of organising the festival was that it should reach a wider public."
Akhmad Kadyrov is being propped up
by Moscow in Chechnya's elections
Organisers are to maintain the screenings at the Andrei Sakharov Centre, named after the Nobel prize-winning human rights campaigner, although with an auditorium of only 90 seats, the festival will reach a much smaller audience.
The programme of 18 films, 12 of them Russian, runs from Thursday to Saturday. It has been organised by local human rights groups such as Memorial and the Soldiers' Mothers Committee and received backing from non-Russian groups such as Amnesty International and Human Rights Watch.
The films provide graphic and sometimes harrowing accounts of the war in Chechnya as seen through the eyes of local people, Russian soldiers sent to the republic to enforce the Kremlin's rule, and their parents.
They include "Assassination of Russia", a documentary funded by the self-exiled billionaire Boris Berezovsky, one of the Kremlin's strongest critics, that accuses the FSB of staging the 1999 apartment bombings that Moscow used to justify launching the current Chechen war.
President Vladimir Putin accused Chechen fighters of being behind the apartment block bombings although no firm evidence to back up that claim was ever produced.
Samodurov said he had suggested withdrawing this film, along with two others known particularly to have angered the Russian authorities, from the Kinocentre programme, but to no avail.
The other offending films were from Britain's Channel Four television: "Terror in Moscow", about last year's hostage crisis in a Moscow theatre in which 129 people died after special forces used gas to stun the hostage-takers, and "Babitsky's War", about a Russian reporter in Chechnya who was kidnapped by the secret services.
"I thought this would be impossible. I'm shocked"
Speaking from London, George Carey, producer of "Terror in Moscow", said that films that gave people a better understanding of why such events happen "can only do good: it's suppressing information that's harmful, and usually a sign that the authorities feel they have something to hide."
The festival comes in the run-up to Sunday's poll in Chechnya which Russian authorities are presenting as proof that the military phase of the counter-insurgency operation launched exactly four years ago is over and that normality has returned to the republic.
Chechen separatist fighters and other critics have contested the legitimacy of the poll, arguing that it is taking place in conditions of military occupation and that the lack of serious rivals to the Kremlin's favoured candidate, Akhmad Kadyrov, have reduced it to a farce.