Hours after the attack on Friday, a spokesman for the SVR foreign intelligence service ruled out any involvement in the blast that killed three men and injured Yandarbiyev's son.
Boris Labusov said the SVR "has not taken part in such actions since 1959," when a Soviet KGB agent in Munich assassinated Stepan Bandera, a Ukrainian nationalist.
Russia has two main foreign intelligence agencies, the SVR and the GRU military intelligence service.
But a top Chechen rebel charged that Russian authorities were responsible for the attack.
"There is no doubt that [President Vladimir] Putin's regime is behind this," said Ahmad Zakayev, a spokesman for former Chechen president Aslan Maskhadov.
"A presidential election is going on and as everybody knows he [Putin] came to power on the blood of the Chechen people."
Putin launched Russia's second war with separatist Chechnya as prime minister in October 1999 and was elected president five months later on the back of popular support for the campaign.
The SUV the former president had been driving was unrecognisable. Yandarbiyev's injuries were so bad that he died on the way to Doha's Hamad hospital.
Police have not given any details except to confirm the death and identity of the former separatist leader.
Living in exile for the last three years, Yandarbiyev was the first nationalist from the breakaway republic to be added – at Russia's request - to a UN list of groups with suspected ties to Usama bin Ladin and his al-Qaida network.
Yandarbiyev was dead on arrival
at Doha's Hamad hospital
Qatar repeatedly refused Moscow's request to extradite the rebel leader.
However, the Gulf state had made his residence conditional on avoiding international attention and cutting his connections with the Chechen resistance movement.
But on 9 February, the Russian federal security service (FSB) said it was impossible to wage an effective war on terrorism if Chechen separatists could "calmly sit tight" in various countries around the world.
Deputy FSB head Vyacheslav Ushakov publicly insisted that Ahmad Zakayev, Movladi Udugov and Yandarbiyev all be handed over to the Russian authorities.