Sulim Yamadayev once led an elite division of Chechnya's security forces
The authorities in Dubai have accused a senior Chechen official of being behind the apparent killing of a rival of Chechen President Ramzan Kadyrov.
Police said Sulim Yamadayev was shot dead on 28 March. However, there has been confusion over whether he died, with his brother saying he survived.
Two suspects have been arrested, one of whom has implicated a Chechen member of Russia's parliament, Adam Delimkhanov.
Mr Delimkhanov rejected the allegations and accused police of incompetence.
Mr Yamadayev was once close to the president of Chechnya, but fell out with him last year and fled Russia.
The apparent killing was the fourth of a prominent Chechen since September, when Mr Yamadayev's brother Ruslan was shot dead while driving in central Moscow.
The Chechen leader has denied any involvement in the killings.
Speaking at a news conference on Sunday, Dubai police chief Lt Gen Dhahi Khalfan Tamim said an Iranian and a Tajik connected to Mr Yamadayev's killing were in custody, and that four other suspects had fled to Russia.
He said one of the men in custody had admitted to receiving the weapon used from a guard of Mr Delimkhanov, a member of Russia's lower house of parliament and an associate of Mr Kadyrov.
"Our investigation found [Delimkhanov] to be the mastermind of the assassination of Sulim Yamadayev," he said.
Gen Tamim said his force would seek Interpol's help in arresting Mr Delimkhanov and the four other suspects.
"The crime... is 100% of Chechen making and it's an operation of settling accounts," he added.
Mr Delimkhanov said the accusation by the Dubai police chief was a "provocation" aimed at destabilising Chechen society, but that he was willing to answer investigators' questions.
"I am ready to co-operate with the investigation, ready to answer objective and clear questions, if the Dubai police have any," he told Russia's Interfax news agency by telephone.
Last week, Dubai police said Mr Yamadayev had been in Dubai on a Russian passport issued in the name of Sulaiman Madov, and that he had died instantly in the shooting in a car park outside his apartment.
However, after news of his apparent death emerged, Mr Yamadayev's family members told the BBC and Russian media that he had survived, while other reports said he had been buried on Wednesday.
Mr Yamadayev was a separatist rebel leader during the first Chechen war of the mid-1990s who later switched to the Russian side, after Moscow sent troops back into the republic to retake control.
He then became commander of the elite Vostok security forces battalion, a unit of former rebels who have helped quell separatist resistance. In 2005, he was named a Hero of Russia, the top national honour.
But last year, Mr Yamadayev was dismissed after falling out with Mr Kadyrov. He later fled to Dubai after the killing of his brother.
Critics have accused Mr Kadyrov and his supporters of systematically removing any opposition to his rule.
In January, Umar Israilov, a former bodyguard for Mr Kadyrov who had accused him of torture and kidnapping, was killed in Vienna. The next month, a former deputy mayor of Grozny was shot dead in Moscow.