WASHINGTON — Rich industrial countries are likely to try to promote economic cooperation among the Soviet republics and support the new commonwealth now that the Soviet Union has all but ceased to exist, Western officials said.The Group of Seven (G-7) nations want to prevent an outbreak of economic warfare in the Soviet Union, with individual republics erecting trade barriers against one another. Deputy finance ministers from the G-7 - Britain, Canada, France, Germany, Italy, Japan, and the United States - met over the weekend to review the world economy and discuss how to react to the virtual disintegration of the Soviet Union. The G-7 wants to make sure the ambitious economic reform program planned by Russian leader Boris Yeltsin does not trigger a protectionist response from the other republics. Some of the Soviet republics recognize the problem and are already working together to prevent it under the aegis of the newly formed commonwealth. Normally, the International Monetary Fund (IMF) would provide financial support to a state such as Russia that is pursuing economic reforms. But it cannot because none of the Soviet republics are an IMF member. In July, the Soviet Union applied for membership of the IMF. But the country has since broken up. The commonwealth accord makes membership for individual republics more likely. Until that occurs, however, the onus for supporting the republics' reform efforts will fall on the West. Experts suggest that may be why Washington has called for an international conference next month to discuss the Soviet Union's needs in order to spread the burden as much as possible.