UPDATE 1-Georgia and Russia at odds after Caucasus talks

* Two sides conduct war of words after one-day talks

* Session coincides with Russian military exercises

(Recasts after Georgian, Russian press conferences) By Laura MacInnis and Stephanie Nebehay GENEVA, July 1 (Reuters) - Georgian and Russian officials clashed publicly on Wednesday after one-day talks aimed at avoiding further conflict in the volatile Caucasus region.

Grigory Karasin, Russian deputy foreign minister, declared that Georgia's territorial integrity was "only virtual in nature" following their five-day war last August.

His Georgian counterpart Giorgi Bokeria described Russia's ongoing military exercises in the region as a "potential threat" and called for international police to be deployed.

Still, international mediators put a brave face on the sixth negotiating session held in Geneva since last October, saying the closed-door discussions had been strained but constructive.

Talks to prevent a repeat of last year's flare-up would continue despite heightened Moscow-Tbilisi tensions, a joint statement by mediators from the European Union, United Nations and Organisation for Security and Cooperation in Europe said.

More negotiations will take place in Abkhazia's eastern Gali region on July 14 and in Geneva on Sept. 17, they said.

In Wednesday's talks, both sides skirted the issue of the future status of Georgia's breakaway territories, South Ossetia and Abkhazia, which Moscow recognised as independent states after crushing a Georgian assault on South Ossetia last August.

But the gloves came off at their separate press briefings.

"Unfortunately to our great regret Georgia is refusing to recognise the basic realities and is continuing to act as if these negotiations are conducted with Russia and the international community but in no way, shape or form with Abkhazia or South Ossetia," Karasin said.

SECURITY VACUUM

Tensions remain high nearly a year on from the Caucasus conflict, after which Russia stationed thousands of troops in South Ossetia and Abkhazia.

Earlier this week, Moscow raised Georgian stress levels by launching large-scale military exercises in its strategically important southern region [ID:nLT135192].

"We consider that as a very threatening step accompanied by hostile rhetoric and continous propaganda about an alleged Georgian threat," said Bokeria, first deputy foreign minister.

"So that propaganda about an alleged Georgia threat combined with massive military manoevres just like one year ago pose a potential threat. We hope this threat will not materialise."

But Bokeria said the talks had provided an opportunity to "discuss the most important issue, new security arrangements on the ground" and the "non-use of force".

U.N. monitors began pulling out of Georgia and the OSCE closed its observer mission on Tuesday, raising concerns about a security vacuum in the key transit territory for Caspian gas and oil where a five-day war erupted in August 2008. [ID:nLU99002]

The United States, Georgia's ally which sent a delegation, said "nearly all participants" had acted constructively in the Geneva talks on stability and humanitarian issues.

Still, U.S. envoy Matthew J. Bryza said that South Ossetia's participants had refused to host talks on preventing security incidents, demanding instead "as a precondition that Georgia recognise the independence of South Ossetia".

U.N. mediator Johan Verbeke said that the talks "set the groundwork" for future agreements on avoiding use of force in the region and on the role of international security forces.

Russia previously rejected extending the mandates of some 130 U.N. monitors in Akbhazia and 20 OSCE monitors who operated in rebel South Ossetia until last August's war.

Karasin said on Wednesday that Moscow was ready to look at other forms of new missions not directly involving the status question, adding, "We believe that all is not lost." (Editing by Louise Ireland and Richard Balmforth)