As the Aeroflot jet bound for Havana rolled away from the gate at Sheremetyevo airport, the question became: was he ever even really here?

For more than 24 hours the sprawling international airport on Moscow's northern outskirts was the site of an intricate game of cat-and-mouse. The target: Edward Snowden, sought by an enraged US, which has charged him with leaking classified documents on US surveillance programmes and warned countries suspected of abetting his escape.

The action culminated at 2pm on Monday afternoon outside gate 28, where Snowden was checked in for a flight to Havana, another stopover en route to Venezuela or Ecuador, where he had sought political asylum.

Dozens of journalists assembled at the window, hoping to spot the man who had eluded them for endless hours inside Sheremetyevo's winding halls. Hours later, they imagined, they would have Snowden cornered, ready to spill his innermost thoughts as the plane hurtled towards Havana for a full 12 hours.

The news zoomed through the hall – Russian news agencies reported that Snowden and his travelling companion, Sarah Harrison of WikiLeaks, had checked into seats 17A and 17C. Those seated nearby were giddy.

As the plane started to board, more than a dozen Aeroflot agents converged on the gate and ushered reporters away from the windows.

They threatened to confiscate cameras and telephones, and attempted to block the view. Some journalists said they were ready to hide their telephones in their pants. Anything for a snap of Snowden.

One by one, the journalists got on board – all the world's media, and Russia's too. The line dwindled to a crawl and the Aeroflot agents began to whisper: "He's not on board."

The gate closed. A detachable staircase pulled away from the aircraft. The Airbus began to roll backward. "He's not on board," said Nikolai Sokolov, an Aeroflot gate employee, his eyes wide. "I was waiting for him myself."

Around two dozen journalists settled in for the 12-hour journey to Havana – a flight on which no alcohol is served, much to the chagrin of the reporters, many of whom aren't used to going half a day without a stiff drink.

And, yet again, Snowden was nowhere to be found.

He was reportedly in Moscow for 21 hours but no photographs or video of him have emerged – no leaks from the Federal Security Service or police, who use the website Life News to broadcast the news they want the world to see.

Moscow has made its overtures to Snowden obvious, with Vladimir Putin's spokesman, Dmitry Peskov, repeatedly saying the Kremlin would consider an asylum request from the American, as it would from any other. But the events come amid the worst Russian-US relations since the end of the cold war, with the Kremlin once again making anti-Americanism a central governing pillar. The sight of a US whistleblower, hounded by his own government, being welcomed on Russian soil would be nothing short of a coup.

But was he ever here?

When it emerged on Sunday morning that Snowden had boarded Aeroflot flight SU23 from Hong Kong to Moscow en route to an undisclosed third country, journalists streamed towards the airport. They shoved pictures of Snowden into the faces of disembarking passengers, asking: "Have you seen this man?"

Most shrugged and pushed on through the crowd. Two Spanish men, transiting through Moscow en route to Madrid, thought that maybe one of them had. It was the first suspected sighting of a man who would become a ghost.

Russian news agencies jumped into the story, issuing a host of contradictory information by citing an endless stream of anonymous sources. "Snowden is in the transit area!" "Snowden has been examined by an Ecuadorian doctor." While the Hong Kong-Moscow plane was still in midair, somewhere over the Siberian city of Omsk, the Kremlin's English-language channel, Russia Today, flashed: "Snowden already in Russia – SOURCE."

Journalists were not alone in waiting for Snowden. Outside the transit area in terminal F, a grey branch of the airport that remains frozen in Soviet times, plainclothes officers attempted to blend in. As the day wore on, more and more arrived, some following reporters from a distance, others guarding heavy doors that appeared to lead nowhere.

Snowden is believed to have landed in Moscow shortly after 5pm on Sunday. Lacking a Russian visa, and stripped of his US passport anyway, he could not leave the airport. That left the Capsule Hotel, a newly opened site in Sheremetyevo's terminal E, featuring sparse suites with room for little more than a bed. Receptionists there examined photos of Snowden and said they had never seen him.

As evening began to fall, Ecuador's ambassador to Moscow arrived. He too was seeking Snowden (the country's foreign minister later said it had received an asylum request). He did not know where to find Snowden. He was still waiting in the airport, empty of its daytime rush, at 2am on Monday. It was unclear whether he had, at that point, achieved his goal.

The comparisons began to roll in. It was like that Tom Hanks movie The Terminal, about a stateless man stuck in New York's JFK airport.

Or like that other Tom Hanks movie, Catch Me If You Can. The overtones of Waiting for Godot, about expecting the arrival of a man who never arrives, were, perhaps, too obvious.

Nothing like that was to come. Those chasing Snowden resorted to following ridiculous leads – was that group of Russian agents milling around a handicapped people's bathroom hiding Snowden? That airport employee, rolling a tray with three plates, was she about to feed Snowden, Harrison and an unknown third party? That man with the sunglasses, he kind of looks like him, doesn't he?

By 4pm on Monday, after spending 27 consecutive hours inside Sheremetyevo's barely air-conditioned halls, Lidia Kelly, a journalist with Reuters, squinted her eyes in the direction of an overweight senior citizen and asked: "Wait, is that Julian Assange?"

The hunt for Snowden continues.