One of the killers shot at the bodies on the ground, then calmly drove away

Nothing much happens at the small teahouse in Zeytinburnu, a down-at-heel district teeming with refugees and immigrants on the European side of Istanbul. For 15 years, the same group of Turkish men has gathered every day to smoke, play cards and discuss football.

But on 16 September at 2:42pm, they heard a series of dull thuds. Looking out of the teahouse window, the owner saw three men crumple to the ground beside a black car. Then a man got out of the car and shot several times at the bodies.

"He was maybe 50, and of pale complexion – not Turkish," the proprietor remembers. "He was very athletic, jumping around as he was shooting, though he didn't look panicked. Then he got back in the car, and it drove off, calmly."

The three men lay on the pavement, their blood spreading across the stones in thick rivulets. Two of the victims had been shot in the head and were clearly dead, while the third appeared to be still alive. His left hand was twitching slightly and one member of the small crowd found a faint pulse. But by the time the police and ambulance arrived ten minutes later, he too was dead.

The main target of the attack was clearly Berg-Khadzh Musayev, a rebel fighter with the Caucasus Emirate. He was not, as Russian media have claimed, the notorious Amir Khamzat, deputy to Doku Umarov, Russia's most wanted man. But he was a high-ranking fighter, as a photograph of him flanking Umarov testifies. Musayev had come to Istanbul about 18 months earlier, according to Chechen sources in the city, for treatment to an injury sustained in a clash with Russian forces. A video taken just after the injury occurred shows a horrific open wound on Musayev's arm, with a chunk of flesh the size of an apple missing. The separatist fighter is smiling faintly and reciting verses from the Koran.

The other two men shot outside the teahouse, both from the same village in Chechnya as Musayev, appear to have simply been in the wrong place at the wrong time.

A source close to the investigation divulged to The Independent what Turkish police think they know so far. They believe eight or nine people were involved in the murder, split into three teams: one dealing with reconnaissance, one with organisation and one with execution. A 55-year-old man travelling under the name of Alexander Zharkov appears to have been the overall organiser. He was allegedly aided by a younger, blond man using the name Nadim Ayupov, who left behind a USB stick in his hotel room that held photographs of him posing with a swastika and some badly written poetry.

The source named two of the remaining suspects, a woman known as Maria M, who was photographed slipping out of Turkey from Ataturk Airport in Istanbul the day after the murders, and Ziyuaddin Makhayev, a Chechen with alleged links to the republic's controversial President, Ramzan Kadyrov, although a spokesman denies the pair are close.

Police have collated airport records and GPS data from hire cars to piece together the movements of Zharkov and Ayupov. The latter arrived in Turkey on 1 September, 16 days before the killing; Zharkov arrived a day later. They both rented cars, a black Opel and a white car of unknown make. On 4 September, the two men met at a tram station in a cloak-and-dagger rendezvous caught on security cameras. They travelled to Zeytinburnu and spent several hours walking around checking out the layout of the streets. The next day they returned, apparently to select a place to dump the car after the hit had taken place. That evening, both cars were driven across the Bosphorous to the Asian side, and parked in a carpark in the region of Kadikoy for five days. Police suspect that the killers took possession of weapons and other equipment during this time, possibly by boat.

On 10 September the two men checked in to a one-star hotel in Sultanahmet, Istanbul's main tourist district, a stone's throw from the Aya Sofia Cathedral and the Blue Mosque. A local source, who knew the name of the hotel and spoke with the two men repeatedly during their stay, agreed to speak to The Independent on condition of anonymity.

"It was quite strange. Sometimes he would speak absolutely perfect English using really complicated words, and other times he would talk in a thick Russian accent and pretend he didn't understand anything," the source said of Ayupov. "He had a sense of humour though, and would laugh and joke. The older guy [Zharkov] was much more serious and would just answer 'yes' or 'no' to everything. It was clear he understood English perfectly though." Sometimes the two men did not come back at night, the source said, and other times they came with others, including on one occasion a woman wearing a turban. "Two days before the murder they were asking around for a place to wash their car; they said they wanted somewhere that would do a really good, thorough job."

Late on the morning of the murder, the two cars left Sultanahmet, and the black car driven by the team of executioners parked close by the teahouse, just after midday. The white car waited at the agreed drop-off point. At 2.42pm, the three Chechens left a nearby mosque after prayers, and were gunned down as they crossed the road, with two people shooting from inside the car and a third exiting to fire control shots into the men's heads. The car drove off to the agreed location, where the suspected agents switched cars. The white car meandered around Istanbul before being abandoned in a car park just off Istiklal Avenue, the pedestrianised hub of the city's nightlife.

Acting on a tip off, police sent plain-clothed agents to wait outside Zharkov and Ayupov's hotel. They believe Zharkov came back to the hotel but spotted the agents and fled. Police later raided the hotel room and found Zharkov's passport, Ayupov's USB stick, as well as a gun, night-vision goggles and a pair of binoculars. A local police source said more than 40 plain-clothes agents, some dressed as tourists, were deployed on the streets of Sultanahmet to apprehend the two men, but they managed to evade detection and slip the net, and from this moment on, the trail goes cold.

From Independence Struggle to Jihad

*The Kremlin fought two brutal wars to keep Chechnya under Moscow's control after the break-up of the Soviet Union. The republic's current head, Ramzan Kadyrov, is a former rebel who has been lavishly funded by the Kremlin to rebuild Grozny. Mr Kadyrov opening a skyscraper complex this week to mark his 35th birthday, an event unthinkable a decade ago.

But the leader has also come in for criticism for his dictatorial style, burgeoning personality cult, and alleged rights abuses.

Over the past decade, the bulk of the Chechen rebel cause has morphed from a largely secular movement demanding Chechen independence to more overtly Islamic rhetoric that links the rebels to global jihad movements and seeks to set up an Islamic emirate covering the North Caucasus.

They lost international sympathy thanks to events such as the Nord-Ost theatre siege in 2002 and the Beslan school siege in 2004. In the past two years, their leader, Doku Umarov, has claimed responsibility for a twin suicide bomb attack on the Moscow metro and a suicide bomber at Domodedovo Airport in the capital.

Mr Kadyrov has claimed that the insurgency is funded by Western security services, though analysts say its money comes from international jihad groups and local corruption.