The Carter administration's senior trade policy official yesterday acknowledged the existence of the "seeds of bilateral tension" between the United States and the Common Market but said he saw little prospect of a trade war.

Ambassador Reubin Askew, the U.S. representative for trade negotiations, cited concerns in Europe over American chemical and soybean exports, a steel dumping complaint filed by the leading American producer, and the prospect that any U.S. limit on imports of Japanese cars could encourage Japan to export more cars to Europe.

These issues have been discussed here in the past two days at meetings of Viscount Etienne Davignon, the Common Market commissioner for industry and international markets, and Askew and other administration officials.

Askew said at a meeting with a group of reporters that "a protectionist tide" is flowing here and everywhere else in the world as a consequence of sluggish economic growth. Nonetheless, he said he remains personally opposed to any effort to curb Japanese car imports artificially and expressed the hope "that we can get through [this period] without any trade restraints."

He said that too often trade policy is used as an attempted "quick fix, distracting us from more fundamental problems." If the United States seeks to boost its export trade, "We must make sure that any import relief is justified," Askew warned.

He predicted that in time the U.S. auto industry "will come back and come back strong." Within a few years, "American cars will be cheaper and get better mileage than Japanese cars," Askew said. He cited a study by the Arthur D. Little company projecting import penetration by 1990 down to 10 percent of the market from 28 percent this year.

Askew denied that he and Davignon were engaged in a negotiation on the steel-dumping case initiated by U.S. Steel Corp. last March. The company charged steel producers in seven European countries with dumping products here below the cost of production.

The admnistration had discouraged the filing of the case, which forced the abandonment of a steel trigger-price mechanism designed to discourage sale here of below-cost imports without resort to the dumping suits.

Askew implied that if some acceptable settlement of the U.S. Steel case is achieved, there could be consideration of a revamped trigger-price mechanism that takes more account of exchange-rate fluctuations than did the old system.

But he also gave the impression that the discussions -- which involve governments, the industry and unions -- are a long-way from being settled.

"The [U.S.] industry has been talking about five to eight years of relief," he observed.