* Chechnya's eateries shut down after spiritual leader order
* Outcry from activists who say it is against Russian law
GROZNY, Russia, Aug 18 (Reuters) - The spiritual leader of the Muslim region of Chechnya has ordered that eateries shut down completely for the month of Ramadan, sparking outrage from activists and residents who say it violates Russian law.
Against the backdrop of a spreading insurgency, many fear that growing interest in radical Islam could fuel separatism in the volatile North Caucasus region where rebels are fighting to create a pan-Caucasus state governed by Islamic sharia law.
Chechnya's mufti Sultan Mirzayev said on Wednesday cafes and restaurants must stay closed even after sundown during Ramadan -- a radical move compared to other parts of the Muslim world.
"We can't have smells wafting through the streets and teasing the hungry," Mirzayev told Reuters by telephone.
The holy month of Ramadan, which started on Aug. 11 in Russia this year, requires Muslims to abstain from food and drink until sunset every day.
Residents of the Chechen capital Grozny said this was the first time a total shutdown had taken place, noting that around half of the cafes were working during last year's Ramadan.
The centre of the city was silent on Wednesday as many cafes shut their doors. Only shops and outdoor markets, where many Chechens buy their food, were functioning.
"They could have at least left us a few places where we can get a bite," said Grozny resident Emira Sadulayeva, 32.
The mufti's order has no legal weight but it is likely to be followed because Mirzayev is a respected spiritual leader. He said cafes refusing to comply "would be encouraged to close".
The cafe blackout highlights tension over efforts by Chechnya's firebrand Moscow-backed leader, Ramzan Kadyrov, to enforce Islamic rules that can violate Russia's constitution.
Kadyrov's spokesman declined to comment on the shutdown.
Critics say the Kremlin allows Kadyrov to run Chechnya like a personal fiefdom in return for keeping relative calm in a region still recovering from two separatist wars with Moscow since the mid-1990s.
By comparison, in neighbouring Muslim Dagestan, this year's Ramadan was observed largely in line with traditions accepted in most other parts of the Muslim world, with cafes staying open after nightfall and with no alcohol served.
Dagestan has overtaken Chechnya and nearby Ingushetia as the epicentre of violence as the Islamist insurgency gains momentum. [ID:nLDE66S0D2]
Rights activist and founder of the Chechen Civil Society Forum, Minkail Ezhiev, said the Ramadan shutdown showed that Chechnya was functioning as a state separate from Russia, where the constitution states that religion and state are separate.
"I am totally against the cafes' closure," he told Reuters. "Everything needs to be within the confines of the law that dictates in Russia."
Critics say Kadyrov's large personal militia impose his vision of Islam in Chechnya, where alcohol is banned, women must wear headscarves in state buildings and polygamy is encouraged by authorities.
In July Kadyrov shocked human rights groups when he praised unidentified assailants for targeting women with paintball pellets for not wearing headscarves. [ID:nLDE66724P]
Before Ramadan started, insurgents from the Kabardino-Balkaria region in the North Caucasus said on Islamist web sites that alcohol-sellers would be "eliminated" during the holy month.
(Editing by Maria Golovnina)
(Writing and additional reporting by Amie Ferris-Rotman)