International Bank of Washington reported yesterday a 68 percent increase in profits last year while May Department Stores Co., owner of the Hecht Co. in the Washington and Baltimore areas, listed substantial gains in earnings and sales for the quarter and year ended Feb. 3.

In other earnings statements, Quality Inns International reported a sharp reduction in second-quarter losses and San Juan Racing Association Inc. reported higher earnings, despite losses from its former soccer team here, the Washington Diplomats of the North American Soccer League.

For International Bank, a diversified financial services and merchant banking business, 1978 was a record year. Profits totaled $15.6 million ($2.15 a share) compared with $9.2 million ($1.30) in 1977, as revenues jumped 32 percent to $21.4 million.

In the fourth quarter, IB earned $3.1 million (41 cents) on revenues of $4.3 million compared with profits of $621,000 (9 cents) and revenues of $1.9 million one year earlier.

George Olmsted, IB's chairman, attributed the second consecutive year of record growth to investments in energy production activities, acquisition of a minority interest in property and casualty insurance firms, a consolidation of Caribbean operations and modernization of manufacturing machinery.

In a few months, an IB company plans to market noise control materials based on a new technology that will help reduce the weight of automobiles and add to the potential of future sales growth, Olmsted said.

Property-casualty insurance profits rose to $7.2 million from $5 million in 1977, offsetting a slight decline to $7.7 million from $8 million in industrial group earnings, caused by a three-month strike at a major plant. Life insurance profits grew to $2.4 million from $2 million while finance and leasing losses were trimmed to $31,000 from $204,000.

May Department Stores, based in St. Louis, reported fourth-quarter profits of $54.3 million ($2.42) compared with $47.6 million ($2.11) the previous year, not counting discontinued catalog showroom operations.

Counting earnings from the discontinued business of $400,000 in the recent period and $1.1 million a year earlier, net income was $54.7 million ($2.44) vs. $48.7 million ($2.16). Sales rose to $911.7 million from $762.2 million for the country's second-largest department store company.

For the full year, May profits advanced to $93.2 million ($4.15) from $84.2 million ($3.72) and sales rose to $2.57 billion from $2.26 billion. A loss from discontinued operations in the recent year of $3.2 million cut net income to $90 million ($4.01). A year ago, a similar loss of $300,006 reduced final net income to $83.9 million ($3.71).

San Juan Racing Association, which owns El Commandante race track in Puerto Rico and nine radio stations, said profits soared in the quarter and nine months ended Jan. 31.

Third-quarter profits were $904,330 (26 cents) compared with $308,389 (9 cents) as sales rose to $11.4 million from $9.4 million. Nine-month earnings were $2.8 million (79 cents) compared with $1.5 million (41 cents) and sales were $31.8 million vs. $28.7 million.

The Diplomats, which San Juan has sold, accounted for a loss of $440,032 in the nine months but the sale added $385,715 for a net loss on the soccer operations of $54,317.

The company, whose radio properties include WJMD and WUST in the Washington market, attributed earnings and sales growth to its communications division. San Juan has sold WTMI in Miami for about $1 million and plans to acquire KNUS in Dallas.

Quality Inns International reported its second-quarter loss was cut from $1.7 million to $200,000 and said operatons moved into the black for the first half of its fiscal year.

The Silver Spring lodging chain earned $730,000 (28 cents a share) in the six months ended Feb. 28 compared with a loss of $1.8 million (68 cents) in the same period a year ago.

After reporting the turnaround, Quality Inns' directors declared a dividend of 10 cents a share payable April 16. The dividend will be the second quarterly payout in a row for Quality Inns, which declared its first dividend in December.