More than two weeks after the human rights activist Nataliya Estemirova was murdered, the Russian investigators sent down to Chechnya have made no arrests and the trail is going cold. To those who live there, where dissidents and rivals to President Kadyrov frequently meet a violent death, it is no surprise.

Ms Estemirova, known as Natasha, was snatched in daylight from a street in central Grozny, the Chechen capital. Her corpse was dumped by a road hours later with gunshots to the head and body in the neighbouring southern republic of Ingushetia. The killing made an orphan of Ms Estemirova’s 15-year-old daughter Lana, who friends say now plans to leave Russia. An outraged President Medvedev ordered that her killer to be found.

But despite claims from Alexander Bastrykin, the head of Russia’s Investigative Committee, to have identified “a number of possible suspects” Ms Estemirova’s friends and colleagues are pessimistic. Leaders of Memorial, the group for which Ms Estemirova, 50, worked fearlessly to compile evidence of torture, abduction and killings of civilians by security forces in Chechnya, say that they have little hope of justice.

Svetlana Gannushkina, a member of Memorial’s council who also sits on Mr Medvedev’s new human rights advisory group, told The Times: “We don’t believe they will find the killers and they won’t find the person who ordered it either. They will just find some Chechens somewhere that they can call the killers.”

Memorial has pointed the finger at Mr Kadyrov, a former boxer who rules with an iron fist under the patronage of Vladimir Putin, Russia’s Prime Minister. Ms Gannushkina said: “The totalitarian regime that has been formed in Chechnya is absolutely controlled by Kadyrov and his circle.”

Mr Medvedev dismissed allegations of Mr Kadyrov’s involvement in Ms Estemirova’s killing as “unacceptable” even before an investigation had begun. However, it fits a pattern of unsolved assassinations of people whose only link is that they were all considered hostile to Mr Kadyrov.

This week another opponent had a narrow escape. Isa Yamadayev, who comes from a rival clan to that of Mr Kadyrov, claimed that a gunman had come to his home in Moscow on Tuesday and tried to kill him. In stark contrast to the pace of inquiry into Ms Estemirova’s death, detectives said yesterday that they had already taken a suspect into custody. Mr Yamadayev’s brothers, Sulim and Ruslan, were not so lucky. Both controlled powerful militias in Chechnya. Both are now dead and their forces taken over by Mr Kadyrov. Ruslan died in a hail of bullets last September as his car waited at a traffic light near the British Embassy in Moscow. Sulim was gunned down in March near his home in Dubai, where his family said he had gone into hiding after warnings that Mr Kadyrov planned to kill him.

Detectives in Dubai named Adam Delimkhanov, Chechnya’s deputy Prime Minister — and a cousin of Mr Kadyrov — as a suspect and placed him on Interpol’s wanted list. Mr Delimkhanov, who sits in the Russian Parliament for Mr Putin’s party, United Russia, denied involvement.

Six days later the human rights lawyer Stanislav Markelov and the journalist Anastasia Barburova, who wrote for the campaigning opposition paper Novaya Gazeta, were murdered on a Moscow street. Both Mr Markelov and Ms Estemirova were close friends of Anna Politkovskaya, the Novaya Gazeta journalist who repeatedly attacked Mr Kadyrov and Mr Putin over rights abuses in Chechnya. She was shot dead in Moscow in October 2006 — on Mr Putin’s birthday. Despite international pressure nobody has been convicted of the crime.

Memorial and Ms Estemirova were a constant thorn in Mr Kadyrov’s side. Activists have said that he rebuked her furiously at a meeting last year for criticising his order for Chechen women to wear headscarves in public. They claim that he boasted to her that he was “up to my elbows in blood”.

Mr Putin installed Mr Kadyrov, 32, as part of his strategy to “Chechenise” the struggle to defeat separatist rebels. Analysts say that Mr Kadyrov has grown so powerful the Kremlin can no longer control him.

Mr Kadyrov has threatened to sue Memorial’s leadership for accusing him of Ms Estemirova’s murder. He says that he is personally overseeing the effort to catch her killers — chillingly, he threatened to deal with them “in the Chechen way”. “The President of the Chechen Republic is the first to want this terrible crime solved,” said his spokesman, Alvi Kerimov. “We have much more interest than The Times in finding those who were responsible.”

It is not quite true to say there have been no arrests in the Estimirova case: riot police detained the organiser of a rally in her memory in Moscow last week. Officials said that too many people had turned up.

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