(Adds OSCE comment)

By James Kilner and Chris Baldwin

MOSCOW, May 8 (Reuters) - Georgia's breakaway region of Abkhazia shot down another Georgian spy drone on Thursday, its Defence Ministry said, although Tbilisi immediately denied the allegation from the Russian-backed rebels.

Minutes before the announcement, Georgian President Mikhail Saakashvili had told visiting Russian reporters war between Georgia and Russia over Abkhazia had only narrowly been averted days earlier but remained a real threat.

According to the Abkhazian authorities this was the third Georgian drone shot down in the last five days and in Helsinki the Organisation for Security and Cooperation in Europe (OSCE) called for calm.

"Today at 1705 (1305 GMT) the Georgians grossly violated Abkhazian airspace with a pilotless drone over the Ochamchirsky region," Gary Kupalba, the Abkhazian deputy defence minister, told Reuters by telephone.

"In response to this, anti-air defences were ordered by the defence minister to shoot it down."

Abkhazia is a sliver of land wedged between the Black Sea and the Caucasus mountains. It broke free from Tbilisi in a war after the 1991 fall of the Soviet Union and is now the focus of a bitter row between Russia and Georgia.

Georgia itself is at the centre of a tussle for influence between the United States and Russia over the Caucasus -- a volatile, mountainous region which hosts a major pipeline pumping oil from Asia to Europe.

A senior official at the Georgian Interior Ministry denied there had been any Georgian drones flying over Abkhazia on Thursday.

"The information that a Georgian drone had been shot by separatist forces is not true," Shota Utiashvili, head of the analytical department at the Interior Ministry, told Reuters.

On Sunday, Georgia also denied Abkhazian allegations that the rebels had shot down two of its spy drones, but in April it accused a Russian military jet of shooting down one of its drones.

DENIAL

The Abkhazians say the Georgian spy drones prove Tbilisi is planning an attack, while the Georgians say the rebels and Russia are trying to stir tensions.

Tension between Russia and Georgia have also risen during the last few months over the second Georgian breakaway province of Southern Ossetia, only a couple of hours drive from Tbilisi.

U.S.-educated Saakashvili came to power in Georgia in a peaceful 2003 revolution and has steered the former Soviet state towards NATO, a move which has angered Russia.

Russian soldiers patrol land between Georgian and Abkhazian forces under the terms of a 1994 U.N.-organised ceasefire but it has re-enforced the number of soldiers in the region because it also says Georgia is planning an attack.

But Saakashvili again said Georgia wanted to avoid a war with Russia.

"Several days ago we were very close and this threat remains," Saakashvili was quoted as saying by RIA news agency.

"But for military conflict two sides are needed and the Georgian side does not want this.

Georgia accuses Russia of a creeping annexation of Abkhazia. Russia already hands out passports to people living in Abkhazia and the Kremlin has promised to strengthen direct ties.

Russia says it is merely trying to protect Abkhazia from Georgian aggression and on Thursday said it would consider further increasing the number of soldiers in the region, a move sure to heighten tension.

In Helsinki, OSCE special envoy Heikki Talvitie said: "The OSCE and the chairman in office are trying to create conditions for dialogue and tell everyone not to escalate it further."

Finland holds the rotating chair of the OSCE. (Reporting by Chris Baldwin in Moscow and Margartia Antidze in Tbilisi; additional reporting by Agnieszka Flak in Helsinki; writing by James Kilner in Moscow, editing by Mary Gabriel)

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