* Bodies with gunshot wounds, explosive device discovered
* Security concerns on rise ahead of Sochi Winter Olympics
* Still unclear if killings linked to the Games (Adds regional official, colour, vox pop, more detail)
MOSCOW, Jan 9 (Reuters) - Russia has put security forces on combat alert in the southern Stavropol region after the discovery of five corpses with gunshot wounds and an explosive device there barely a month before the start of the Winter Olympic Games in Sochi.
Stavropol, about 300 km (190 miles) from the Black Sea resort of Sochi, is the gateway to the North Caucasus region, where Russia faces an insurgency by Islamist militants who have threatened to try to prevent the Olympics going ahead.
President Vladimir Putin, who has staked a lot of political and personal prestige in the Games, has already ordered a beefing up of security measures nationwide after suicide bombers killed at least 34 people in separate attacks last month in Volgograd, another southern Russian city.
The corpses were found late on Wednesday in four cars in two separate locations in the Stavropol region.
A homemade explosive device in a bucket was also found near one of the vehicles, according to Russia's Investigative Committee, which said it and the Federal Security Service (FSB) were exploring several possible motives for the crimes.
No other details were immediately available and it was not clear if the killings had any connection to the Sochi Games.
The acting governor of the Stavropol region, Vladimir Vladimirov, told the state Rossiya 24 broadcaster that authorities had taken measures "to annihilate or detain criminals who might have taken part in these cases".
Rossiya 24 reported a sixth body was found in similar circumstances and said two of the victims were local taxi drivers. This report could not immediately be confirmed.
The broadcaster showed footage of uniformed security officers searching vehicles and questioning residents in the region on Thursday.
"It is scary," said Natalia Petrova, a local resident. "We fear for ourselves and we fear for our children."
Putin pledged after the Volgograd attacks to annihilate all "terrorists" in Russia.
The Winter Olympics open on Feb. 7 in Sochi, which is located on the western edge of the mountainous Caucasus region where the insurgents want to carve out an Islamic state.
The head of Russia's Olympic Committee has said Moscow has taken every possible measure to ensure the Games' safety.
Russian forces went on combat alert in Sochi on Tuesday and about 37,000 personnel are now in place to provide security at the Games, Russian officials say. (Reporting by Tatiana Ustinova, Alessandra Prentice and Gabriela Baczynska; Editing by Gareth Jones)