The resolution was one of a series of decisions reached by 112 Confederation delegates who met over the weekend in Grozny, capital of the self-proclaimed republic of Chechenya.
The delegates also resolved to create a common army, "so that the people of the Caucasus can fight off aggressors", according to a Chechen government spokesman, Movladi Udugov. But it is unclear whether the Confederation, a nebulous organization that tried once before in 1918 to form a government, can carry out such resolutions.
Its assembly comprises representatives of 16 ethnic and national groups in the region, including Ossetians, Lesgins, Chechens, Kabards, Abkhazians and other peoples who feel that they have been repressed by the Soviet, and now Russian, empire.
It is not, however, endorsed by all of their governments. Only Chechenya, Abkhazia and the government-in-exile of Georgia's former president, Zviad Gamsakhurdia, have officially recognised it. Gamsakhurdia now lives in Grozny and attended the conference.
Speakers at the conference called for unity among the small republics of the North Caucasus region. The Confederation's president, Musa Shanibov, also said he believed a second Caucasus war was beginning.
The first, fought between Russia and the peoples who now make up the confederation, took Russia more than 50 years to win, at vast human cost, during the 19th century.
The delegates urged bilateral talks with Russia and voted to change their name to Confederation of the Peoples of the Caucasus in order to encourage Russians and Cossacks to join. But most of the rhetoric was anti-Russian.
Chechenya's outspoken president, Dzhokhar Dudayev, said the Confederation was necessary because it offered an escape route from the current "system of totalitarian regimes".
Dudayev also said he believed the Confederation should have led a "just war" for independence from the beginning, when it was reformed in 1989.
"The Caucasus is on fire", Dudayev told a press conference. "It has been burning for seven years. Each day, new fires flame up. I am fully convinced that all these conflicts are directed by Russia".
Independence from Russia was the main goal of the Confederation, Shanibov, told the meeting. That would include removing all Russian troops from the area and rejecting the March 1992 federation agreement, replacing it with a looser treaty of confederation.
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