NEW YORK - Russia , which is home to a sizable Muslim minority, fears that a further deterioration in insurgency-hit Afghanistan could spill over the border into the rest of Central Asia -- and onto its doorstep, a leading US newspaper reported Monday. "If Afghanistan and Pakistan are further destabilized, this instability will flood Central Asian countries and the Russian border and flood the south of Russia ," a retired Russian general was quoted as saying by The Los Angeles Times. "Russia will do anything to prevent that," said Lt. Gen. Ruslan Aushev, who served five years in Afghanistan during the Soviet occupation of the 1980s. The Russian fears of the fallout from the deteriorating situation in Afghanistan and Pakistan form part of the The LA Times dispatch on Moscow's mixed signals as Russia seeks to improve relations with the West by offering help with Afghanistan while trying to maintain control over Central Asia. The Moscow-datelined dispatch opens with the comment: "Russia seems to have a message for the Obama administration: Go ahead and boost your military effort in Afghanistan -- but not without our help". In recent days, the dispatch said, Russian officials have rushed forward to offer logistical help to NATO troops in Afghanistan -- at the same time dipping into a dwindling budget to offer impoverished Kyrgyzstan more than $2 billion in an apparent payoff for ejecting a U.S. military base crucial to the war against the Taliban. "In fact, Russia is tugged between two strong, conflicting impulses. It distrusts U.S. motives, especially when it comes to America's penetration of former Soviet states. But Moscow's sense of invulnerability appears shaken by falling oil prices and the precarious economy," the dispatch said. "Many analysts believe the Kremlin is looking for an opening to make nice with the West. Nearby Afghanistan , where instability also spells danger for Russia , presents a handy opening. "And so Russian officials offer help with one hand, lash out with the other". "They see a menace on the side of America, where it does not exist, and they don't see the real scale, the real magnitude, of the menace from the south, from Islamic fundamentalism, which is a real danger," said Sergei Arutyunov, chairman of the Caucasus studies department at Moscow's Institute of Ethnology and Anthropology. "They pay tentative and not always consistent lip service to American efforts in fighting this menace, but on the other hand they are even more afraid of the American presence anywhere near their borders." The Times noted that Russia needs a more peaceful Afghanistan . "The mountainous Central Asian republics on the Afghan border are tribally and culturally intertwined with Afghanistan , and easily influenced by conflict there. And those republics, in turn, are closely tied to Russia ... "Some analysts criticized Russia 's eagerness to see the United States ejected from Kyrgyzstan', it added. "If Russia really wants to help and assist in the American efforts in Afghanistan , then the Russian government should use its influence not to cajole the Kyrgyz into abolishing this base but, on the contrary, to broaden the abilities of this base as an indispensable, important link in the chain of anti-Taliban operation," Arutyunov said. But others, it said, predicted that Russia would follow up by offering to help the United States supply Afghanistan . And sure enough, Moscow has sent out increasingly broad offers to open its territory for transport. Last week Russia 's foreign minister even dangled the possibility of transporting weaponry to Afghanistan , the dispatch added.