The threat, made in a statement by the Russian Defence Ministry, follows the strafing last month of a Black Sea hydrofoil, many of whose passengers were Russian refugees who were fleeing turmoil in the region.
Yesterday's statement blamed Georgian authorities for the helicopter attack, an accusation denied by the Tbilisi government.
There has been a steady drum-roll of menacing statements from Moscow in recent weeks as fighting in Georgia and Moldova embroiled Russians troops, and Baltic nationalism left Russian settlers feeling increasingly vulnerable. The Russian Defence Minister, General Pavel Grachev, has threatened to 'bring to account' anyone who attacked his men.
The risk of Russia being sucked into the conflicts convulsing the former Soviet republics is perhaps the most dangerous legacy left by the collapse of Soviet power. There are nearly 1.5 million Russian troops still stationed outside Russia's own borders in newly independent states as well as 25 million ethnic Russians.
Boris Yeltsin, the Russian President, under attack from hardline nationalists appalled by the rapid collapse of an empire built up over centuries, faces pressure to take a firmer line in defending not only Russian troops abroad but the substantial Russian-speaking minorities in the former republics. Yesterday's statement made clear that Moscow felt responsible not only for troops stationed outside its borders but also for civilians too.
Georgia for its part insists the attack on the hydrofoil was engineered by Abkhazian rebels keen to sabotage a recent peace settlement brokered by Mr Yeltsin.
Russia has announced that it would double the price of oil in the next few days, a move set to anger consumers already battered by massive inflation but still only a small step towards the world market price.
Mr Yeltsin, keen to dispel concern that his economic reforms are sliding into a quagmire of indecision, yesterday signed a decree ordering the price hike, said a senior economic adviser, Alexei Ulyukayev.