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Lets start from the fact that one of the key aims of the Marshall Plan was "to prevent the spread of international communism" (quoting Alexander DeConde from "Encyclopedia of American foreign policy") which was clearly synonymous to weakening of USSR influences in the European region. Even before the Marshall Plan came into reality, communist parties lost the elections in several Western European countries in the spring of 1947. This way there's no surprise that there was a strong reaction of Soviet Union, who at the same time tried to strengthen their influences in both Western and Eastern Europe.
USSR took a big role in the initial stage of negotiations around the Marshall Plan. Western European politics didn't want to exclude Eastern Europe countries (including USSR) as that could be a clear signal of distrust. What's important, at the beginning Stalin was interested in sharing the profits of the plan, but finally decided it could led to the weakening of control over the economy of Eastern European countries.
As some countries, like Czechoslovakia and Poland were interested in taking help and agreed to take part in Paris convention, 12th May of 1947, USSR decided to act against it. Jan Masaryk, foreign minister of Czechoslovakia was called on the carpet and many people believe that it was one of the reasons why he was killed the next year in what is known as 3rd defenestration (official records counted it as a suicide, but it was later confirmed as a murder during a police investigation in 2004). Polish prime minister JΓ³zef Cyrankiewicz, already being a socialist in opposite to Masaryk (who stood in the government as the only representative of opposition in Czechoslovakia), was rewarded by Stalin with economic help for the resignation from taking part in the Marshall Plan.
This way the only Eastern Europe country that sent its representatives at the talks in Paris was Yugoslavia, where Russian influences weren't as strong, while Vyacheslav Molotov spoke in the name of all countries of Soviet bloc. Also the representatives of Finland didn't come to the meeting, as being a neighbor of USSR they didn't want to risk any problems.
The official statement of USSR was an alternative plan, called the Molotov Plan, which suggested the Russian involvement in providing help to Western European countries. Russian actions to stop the Marshall Plan included also the speech of Andrei Vyshinsky (foreing minister of USSR) to the United Nations, where he accused the plan of violating United Nations' principles.
The main reactions of USSR didn't influence the later existance of Marshall Plan. On the other hand, it influenced communist parties in Western European countries, which were blamed by Stalin for their small role in local societies, even if by not taking any more agressive actions, they were just following his earlier orders. As for Eastern Europe, in two years the Comecon was established and the economic Cold War started.