A Korean buying mission, with plans for on-the-spot orders of up to $2 billion, arrived in this country yesterday as part of an effort to underscore the growing economic relationship betwwen U.S. and Korea.

Korea has become the 13th largest U.S. trading partner, with a two-way trade last year close to $7 billion, which reflected a Korean surplus of about $500 million.

Coincident with the buying mission - which in a three-week period will cover five cities, including Washington - the 9th annual Korea-United States Commerce Ministers meeting will take place here April 10-12.

At that session, Secretary of Commerce Juanita Kreps will meet with Korean Minister Gak-Kyu Choi, who is the leader of the 40-man business-government delegation from his country.

Lee Eun Tak, commercial attache here, said in an interview that Korea is anxious to develop closer ties with the U.S. that will increase American imports to and capital investment in his country. One reason is the need, as Koreans see it, to diversify their imports, and reduce a great dependency on Japan.

U.S. sales to Korea have skyrocketed from $220 million in 1962 - virtually all financed by U.S. aid - to $3.2 billion last year. Korea at the moment is the largest U.S. market for cotton. The U.S.also exports substantial quantities of pulp, ores, scrap metals, machinery and transportion equipment to Korea.

According to the Korean government, more than 100 U.S. companies have made equity investments in Korea, mostly joint manufacturing ventures. But one point of tension is the volume of Korean exports of shoes to the U.S., about $400 million annually and which are now subject to an Orderly Marketing Agreement (OMA), a quota which runs to mid-1981.

U.S. sources said that it was unlikely that the buying mission would actually produce business over and above amounts orginally planned. They see the "mission" technique and the bunching of orders as a good and legitimate public relations ploy to call attention to the two-way nature of trade.

According to a spokesman for the Korean government, the buying mission includes chief executive officers seeking equipment for plant construction, machinery, machinery parts, and industrial raw materials and agricultural products.

Other sources said that the Koreans will be investigating substantial purchases of nuclear equipment. The mission will visit, in addition to Washington, the cities of Seattle, Los Angeles, Chicago and New York.