A Conservative MP who attended a party where friends allegedly chanted Nazi slogans and dressed up in SS uniforms, has apologised for "any offence that was caused" at the event.

Aidan Burley used the social networking site, Twitter, to say he did "deeply regret inappropriate behaviour by some guests at a stag party" he attended and was "extremely sorry for any offence that was caused".

The apology, posted at 12.30pm on Sunday, was sent to the MP's 385 followers but was picked up by the Twitter community and passed around to many others. It failed, however, to assuage those outraged by his behaviour, with many continuing to call for his sacking and resignation.

The 32-year-old Cannock Chase MP was dining at a restaurant in the ski resort of Val Thorens, at Savoie, in the French Alps. Some of his 12 friends in the restaurant chanted "Hitler, Hitler, Hitler", according to the Mail on Sunday.

The paper claimed that the MP, who was elected in 2010, sipped wine while at least one man sitting near him goaded a French waiter, asking: "You are from Germany? No, you must be from Austria, then?" and "Are you insulting his Reich?"

Burley was filmed raising his glass in a toast before, the paper claimed, another guest beside him made a speech, in which he said: "Let's raise a toast to Tom for organising the stag do, and if we're perfectly honest, to the ideology and thought process of the Third Reich."

The party was said to have moved on to a British-themed pub, where partygoers adopted thick German accents and chanted: "Mein Fuhrer! Mein Fuhrer! Mein Fuhrer!", "Himmler! Himmler! Himmler!" and "Eichmann! Eichmann! Eichmann!"

The paper quoted a French police spokesman who said that Burley's friends could face prosecution: under the French penal code it is a crime to wear or exhibit in public anything reminiscent of what was worn or used by the Nazis, unless required for the purposes of a film, play or historical exhibition. The spokesman added: "Anti-Semitic and pro-Nazi crimes are taken extremely seriously in France. Anyone suspected of breaking the law in this respect can and will be prosecuted."

Burley, a rising star in the Conservative party and senior aide to the transport secretary, Justine Greening, was thought to be close friends with the man who wore the SS uniform – Mark Fournier, 34, an accountant and graduate of Queen's College, Oxford University, for whom the stag party was held.

Fournier, the paper added, was frequently addressed by the others as "Himmler". His brother, John Fournier, 37, a businessman, gave the toast. Later, the elder brother gave another speech, saying of Burley: "This man is a Tory MP. He went to Oxford as well. A Tory boy. He was the candidate for Berlin East."

Burley, who was said to be standing a few feet away, was not seen to object to any of the speeches or the actions of his friends, the paper claimed.