Comedy is now diplomacy by other means. A mighty nation has taken to conducting a grave international dispute by means of humour, expecting a similarly comic response in kind. How else are we to view the interview granted with RT, the state propaganda outfit formerly known as Russia Today, by the Morecambe and Wise of the east, the two men who identified themselves as Ruslan Boshirov and Alexander Petrov?

Salisbury reaction: 'It would be comical but for the fact someone died' Read more

Posing as Russian sports nutritionists, a professional fraternity whose record is not entirely unblemished, the comedy duo told the channel that they were indeed the men the UK authorities had identified as visiting Salisbury in March, but they hadn’t made the trip to kill the former spy Sergei Skripal. On the contrary, they were there as wide-eyed tourists, lured by the prospect of seeing a cathedral “famous for its 123-metre spire”. Wasn’t it odd that they had visited Salisbury so briefly on the first of two consecutive day trips? Not at all, the TV funnymen insisted: these strong sons of the Russian winter had had to abandon their first attempt to see the sights, deterred by the impassable Wiltshire slush.

Titter ye not, as fellow TV comedian Frankie Howerd might have put it. But titter we have, as the Boshirov & Petrov show has spawned a thousand parodies. Their purported explanation was laughable and we have duly laughed. But is it the right response?

The question is not confined to Vladimir Putin and his troll state. On Thursday Donald Trump claimed that 2,975 people did not die in Puerto Rico from last year’s Hurricane Maria, despite the meticulous analysis that had led his own government to arrive at that figure. Trump tweeted that the death toll had been invented by “the Democrats in order to make me look as bad as possible”.

What is the best way to deal with these egregious assaults on truth by two of the world’s most powerful men, one an authoritarian autocrat, the other a would-be authoritarian autocrat?

Laughing in their faces has great appeal. It avoids dignifying garbage with a serious reply and rightly pricks the bubble of grandiosity that envelops all dictators, both actual and aspiring. But it comes at a cost. Lost in all the spire gags, for example, is the fact that the two Russians are credibly accused of using chemical weapons on British soil – and that a woman, Dawn Sturgess, is dead from novichok poisoning.

More to the point, and though it sounds po-faced, to laugh at the RT interview is to risk collusion with it. Putin surely knows this alibi of his is absurd and easily debunked, and yet he offers it anyway. Part of that is the usual Kremlin trick: the weaponisation of doubt, throwing up enough chaff to enable Russia’s defenders to say the picture is unclear, the truth is elusive and no one can ever really know for sure.

But it’s also more brazen than that: offering up a risible explanation whose very implausibility confirms that Moscow simply doesn’t care. The humour is intended to humiliate Britain: we killed on your territory and now we are laughing at you. To which Downing Street’s unsmiling condemnation of Russia’s “lies and blatant fabrications” may well be the right reaction.

In that spirit, perhaps the best way to reply to Putin and Trump is with a calm, methodical debunking of their falsehoods. In the Salisbury case, CCTV sightings of the two men have made that easy. This approach has the virtue of winning over the undecideds, including within international opinion, as they watch Moscow and London slug it out. There is also a moral dimension: lies should not be allowed to stand without rebuttal.

Play Video 1:24 Men claiming to be Salisbury novichok attack suspects speak to Russian state TV – video

But here too there are problems. Defeated on the first hundred facts, the most ardent defenders of the Kremlin narrative will simply move on to the next hundred: their ingenuity in explaining away hard evidence is a bottomless well. It also risks a descent into what my colleague and longtime Putin-watcher Luke Harding calls “Versionland”, in which there is no single truth grounded in fact but competing versions.

At best, even if you regard debunking as a necessary exercise it is hardly sufficient. The media has a special responsibility here, and there are small, specific actions we should take. Denying a megaphone to the likes of Alex Jones – who claims, without evidence, that the Sandy Hook massacre of elementary school children was faked – is a welcome first step.

But news organisations need to drop the assumption when covering either Trump’s White House or Putin’s Kremlin that they are dealing with actors who play by the accepted rules of fact and veracity. That means you can’t simply tweet out a headline saying “Trump: 3,000 did not die” without effectively spreading his lies for him. And it means you can’t give the 8.10am interview slot on Radio 4 to a man presented as a fellow journalist when that man is in fact a functionary of the Russian state. Still, we will have to go further.

In a thoughtful new book, Denial: The Unspeakable Truth, Keith Kahn-Harris draws a useful distinction between traditional denialist movements – which sought to construct “towering edifices of pseudo-scientific evidence” to support their claims – and what he calls post-denialists, who are much more cavalier. Rather than make a detailed case like, say, the climate-change deniers of old, post-denialists simply assert.

Putin on Salisbury and Trump on Puerto Rico are perfect examples of this new post-denialism, says Kahn-Harris. They are in the business of “asserting their power to shape reality according to their will”. Casting aside the niceties of facts and evidence, post-denialists are inching closer to saying what they really think: while an old-school Holocaust denier would say Auschwitz never happened, a post-denialist might say it did – and that it was good. On this reading, Putin is getting closer to saying: “Sure, we did Salisbury: what of it?” With Trump, it’s, “Puerto Rican lives matter to me less, because their skin is the wrong colour.”

If this is what’s happening, it requires a different response. It means getting to the heart of the matter, tackling the underlying, if repugnant, belief rather than focusing on the facts, or gags, that lie on the surface. It means responding to Trump not with data, but with a moral argument for the equal worth of all human life – and to Putin with the moral case against chemical weapons.

Perhaps that does not feel like the struggle for today. But it is fast becoming one of the urgent questions of our time: how do we defend the truth in a world of lies?

• Jonathan Freedland is a Guardian columnist