GROZNY, Russia, March 10 (Reuters) - The pro-Moscow Chechen government has started to demand that female state workers wear headscarves, women in the turbulent Muslim region said on Friday.

"I received a verbal warning that if I did not wear a headscarf, I would lose my job. I had to wear it the next day so as not to bring trouble on my head," said one woman who works in the regional administration and asked not to be named.

A spokesman for the region's new prime minister, Ramzan Kadyrov, who has pushed through a series of Islamic decrees, denied the headscarves were compulsory and said women were merely encouraged to cover their hair.

But women used to the rough tactics of Kadyrov's government, which is accused of mass abduction and torture in its hunt for separatist rebels, took the suggestion as law.

Kadyrov was appointed prime minister last week, but has effectively ruled the region since late 2005. He has cracked down on alcohol sales, banned gambling machines and barred Danish aid workers after the global uproar over Danish cartoons of the Prophet Mohammad.

At a meeting with students earlier this month, he unexpectedly gave nine young women who arrived with their hair covered $1,000 each -- a vast sum in an impoverished region.

"We want to return to the culture and beautiful traditions of the Chechen people. The headscarf is just part of this," said a spokesman for Kadyrov.

Analysts say Kadyrov may be pushing through Islamic decrees to try to steal support from the rebels, although his officials say he is simply doing his duty as a Muslim.

The separatists who ruled Chechnya until Russian troops unseated them in 1999 imposed elements of Islamic Sharia law which Russian authorities then scrapped as contrary to the secular constitution.

Some officials have raised concerns over Kadyrov's imposition of Islamic laws in Chechnya but most accept there is little they can do about it, since the 29-year-old prime minister's grip on power in the region is complete.

Many Chechen women wear headscarves anyway, particularly outside the regional capital Grozny.

Some said they should be allowed to choose for themselves.

"I think we live in the modern world, and I myself should worry about my external appearance. These people making laws about fashion should get involved with other problems, which we are not short of," said one 38-year-old Chechen woman.