The State Bank of India, the largest commercial bank company in that country with assets of more than $13 billion, has opened a representative office in Washington.

Joining about a half-dozen other foreign banks with offices in the District's growing international financial center downtown, State Bank of India will act as an intermediary in negotiations with such institutions as the Export-Import Bank on transactions involving India's government and business.

The bank, with 5,000 offices in India, is one of the world's 100 largest commercial banking enterprises. Three other offices are located in the U.S. money market centers of New York, Chicago and Los Angeles.

State Bank handles roughly half of India's foreign trade, which now exceeds $20 billion, according to A. K. Puri, who heads the new Washington office at 1735 K St. NW. He was joined by the bank's chairman, P. C. D. Nambiar, at a reception for the financial community here on Thursday night.

Most other foreign banks with offices here are based in South America or Japan and local bankers expect a number of European institutions to open offices here in the next few years -- with the possibility of establishing full commercial bank branches considered likely.