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.