In an attempt to stem pressure for European Economic Community restrictions on imports of Japanese-built cars, Japan promised West Germany today to limit its car exports to that country to not more than 10 percent above last year's level. The pledge made to Otto Graf Lambsdorff, the West German economics minister in Tokyo today was welcomed by Chancellor Helmut Schmidt, who met the Japanese prime minister, Zenko Suzuki, for talks in Hamburg today.

Suzuki is on the first stage of a 12-day tour of Europe -- the first by a Japanese leader for eight years.

In 1980, Japanese car exports to West Germany rose by 70 percent. For the first quarter, they were 31 percent above the total for the same period last year. To achieve the 10 percent limit, exports for the rest of the year will have to be cut considerably.

The agreement with West Germany is they first concrete Japanese concession since last month's voluntary restraint agreement with the United States, under which the Japanese promised to hold car exports to the United States to 1.7 million this year (120,000 fewer than last year).

Last week, Japan refused to curb its exports to the EEC but offered to discuss the problem with individual countries. Japan has a growing trade surplus with the EEC; its worsened by 46 percent in the first four months of this year.

After more than six hours of talks with Suzuki, Schmidt said tonight that he agreed with his Japanese guest that they both had to fight against protectionism and against attempts to limit free trade. A Japanese economic delegation is to visit Europe soon to learn at first hand of the problems European exporters encounter in their business with Japan.