President Carter has assured the Common Market privately that Congress will extend the waiver of countervailing duties against subsidized imports when it reconvenes in January.

Diplomatic sources said the President gave the assurance in a letter to Roy Jenkins, president of the executive commission of the nine-nation European Economic Community.

In the letter, which was sent apparently to the leaders of the free world's major economic powers as well, Carter said "I am confident that I can secure extension (of the waiver) from the new Congress in January."

At the same time, the President warned that a breakdown in the current world trade negotiations would imperil the economic growth of Western nations. He said the economic expansion goals set forth last summer at the Bonn summit "would of course be jeopardized by the failure of the multilateral trade negotiation."

The leaders of the free world's seven major economies - the United States, West Germany, Japan, France, Great Britain, Canada and Italy - agreed at the summit that the reforms being sought in the Tokyo Round of trade negotiations were "one of the driving forces for more sustained economic growth."

Common Market leaders have been warning of a major trade war unless Congress extends the President authority to waive countervailing duties against imports that are subsidized by foreign governments. The current waiver authority expires Jan. 3.

Carter, in his letter to Jenkins, assured the Common Market that "I did everything possible to secure the extension of the countervailing duty waiver."

The President also used the letter to outline his administration's new anti-inflation program, expressing the hope that the program would hasten the reduction of the U.S. trade deficit.

European diplomatic sources reacted to the Carter letter with a wait-and-see attitude. They argue that it was internal U.S. actions that created the current trade impasse and, as once source said, "it is now up to the Americans to deliver."