(Adds mayor, police saying 3 killed)
By Steve Gutterman
MOSCOW, Dec 27 (Reuters) - A car bomb killed three people in the southern Russian city of Pyatigorsk on Friday, officials said, in a worrying development for the Kremlin as Russia prepares to host the 2014 Winter Olympics in Sochi in six weeks' time.
Pyatigorsk lies 270 km (170 miles) east of Sochi, where the Games, a major prestige project for President Vladimir Putin, will open on Feb. 7.
The blast blew out the windows of buildings in an industrial neighbourhood of the spa resort town, officials said. Thee people were killed, Pyatigorsk mayor Lev Travnev said on state-run Rossiya-24 television.
The explosion badly damaged a traffic police building, Interfax news agency reported, but state-run Itar-Tass cited police as saying all three people killed were bystanders, not police.
Pyatigorsk is just north of a strip of mostly Muslim provinces plagued by near-daily violence in a long-running Islamist insurgency. Its leader, Chechen warlord Doku Umarov, urged militants in a video posted online in July to use "maximum force" to prevent Putin staging the Olympics.
Militants say they want to carve out a Muslim state in the North Caucasus. Their insurgency is rooted in two post-Soviet separatist wars in Chechnya, one of the region's provinces.
Putin has staked his reputation on a safe and successful Games and ordered law enforcement agencies to improve security in the region.
Nobody immediately was blamed or claimed responsibility for the bombing in Pyatigorsk. Militants based in the North Caucasus have carried out some of their deadliest attacks beyond its borders, in the Russian heartland.
Suicide bombers killed 40 people in the Moscow subway in 2010 and 37 at the Russian capital's busiest airport in 2011. A suicide bomber killed six people in October on a bus in the southern city of Volgograd. (Editing by Mark Trevelyan)