Boosted by heavy Soviet purchases of American grain to offset a bad 1977 harvest, Soviet-American trade turnover reached $2.78 billion in 1978, the highest total so far recorded between the two countries.

According to figures released Tuesday by the U.S. Embassy Commercial Office, the 1978 turnover is about 50 percent higher than the 1977 total of $1.85 billion, and about $300 million higher than the previous record-setting total of 1976.

Last week, President Carter sais he hoped to extend most-favored-nation trade status to the Soviet Union and the Peoples Republic of China within the next few months, with congressional approval. The MFN status reduces tariffs and makes obtaining credit easier, a goal long-sought by Moscow. The Jackson-Vanik Amendment to the 1974 Trade Act tied improved trade status with eased Soviet restrictions on Jewish emigration, and Carter said the Soviets had increased their emigration in 1978, when 30,300 Jews were allowed to leave the U.S.S.R.

Western analysts here said the record trade turnover for 1978 was due to a 62 percent increase in Soviet purchases of agricultural products to $1.68 billion from $1 billion in 1977.

At the same time, Soviet purchases of nonagricultural products such as machine tools, tractor parts, drilling equipment and temperature-control devices declined about 4 percent to $562 million from $586 million in 1977.

The analysts consider this category somewhat more representative of Soviet trade capabilities because it covers items the government trading organizations want rather than what they are forced to buy because of harvest reversals. The record 1978 Russian grain crops and should mean substantially reduced grain purchases in 1979 by Moscow.

Carter's address last week signals another step by the administration to improve the climate for trade between Moscow and Washington. Last December, Treasury Secretary W. Michael Blumenthal headed a U.S. trade delegation here that emphasized administration interest in repealing the Jackson-Vanik Amendment once a new strategic arms limitation agreement had been signed between the governments and ratified by the U.S. Senate.

Perenially strapped for hard currency to pay for Western purchases, the Soviets have considered the Jackson-Vanik Amendment a major barrier to improved trade.The government newspaper Izvestia reiterated that view Monday in a blunt article which declared in part that "people forget that pressure on the Soviet Union has never yielded any results."

The commentary asserted that "competitiveness of U.S. firms is being limited for artificial reasons, and trade with the Soviet Union is going down.... Progress in trade will not have a stable character if it is tied to factors of a short-term nature." The Soviet have maintained that trade restrictions are more harmful to the U.S., with its balance of payments deficit than to the U.S.S.R. These public pronouncements never mention the Soviet Union's own trade deficit with Western nations, which now exceeds $15 billion overall.

Total U.S. exports to Russia stood at $2.24 billion for 1978, a 38 percent increase from 1977. Americans imported $540 million from the Soviets, with gold for nonmonetary purposes the largest single item, at $285 million. Other major U.S. imports were fuel oil, aluminum waste, diamonds and sable pelts worth $7.8 million.

The U.S. and Soviets are discussing a wide range of new projects from a jeans factory to a massive steel smelting works to a modernization of antiquated Soviet car factories. Some of these projects may reach contract stage this year and eventually would push the trade figures higher. Among the steps taken by the administration to improve trade relations was White House approval, after months of controversy and delay, of a Dresser Industries oil drill bit manufacturing plant for hard-rock well sites.