International Bank, a merchant bank with investments in manufacturing, insurance, finance, leasing, off-shore banking and various services, said yesterday that profits declined to $1.2 million (9 cents a share) in the first quarter from $4 million (32 cents) last year. Revenues tumbled to $3.7 million from $5.9 million.

Earnings also fell at Flow General Inc., but they rose at the Rouse Co.

Commenting on the D.C. bank company's performance, Chairman and Chief Executive George Olmsted said "the steep recession has depressed sales of our industrial products. Competitive market conditions. . .and higher frequency of claims. . .produced underwriting deficits" in IB's insurance operations. "Higher interest rates have drastically curtailed housing construction and automobile production--activities served by our manufacturing operations," he said.

Rouse Co., which turned in strong first-quarter performances by its retail centers--in contrast to declines felt by much of the retail industry--posted a 156 percent gain in profits over the same period of 1981.

Earnings were $1.69 million (82 cents a share) compared with $659,000 (5 cents) last year. Revenues grew to $37.4 million from $30.9 million.

Company officials yesterday attributed part of the gains to "substantial contributions by interest savings and investment income, resulting from the use of $36 million in proceeds of the private placement of common stock" late last year.

Before noncash charges, earnings by the Columbia-based company's retail centers grew 19 percent over 1981's first-quarater figures.

Flow General Inc., a McLean-based diversified scientific research and manufacturing firm, blamed its drop in third-quarter earnings on poor economic conditions, federal budget cuts and federal indictments on fraud, bribery and conflict-of-interest against employes of one of its subsidiaries.

The company had profits of $5.1 million (61 cents a share) on revenues of $95.3 million for nine months compared with profits of $5.2 million (72 cents) on sales of $79.6 million in 1981. For the latest quarter ended March 31, Flow reported earnings of $389,000 (5 cents) on revenues of $34.5 million compared with $1.9 million (25 cents) on sales of $31.4 million in 1981.

President Joseph E. Hall said recently the earnings problem is "something we'll ride out. As we see it, it's a short term problem."

But the research company president said for its previous growth to continue, the economy must improve, interest rates will have to drop and the dollar will have to lose some strength against other currencies. In addition, Hall said he hopes for a favorable ruling on the federal charges scheduled for trial on May 24 in U.S. District Court in Alexandria. The charges are in connection with an Army procurement contract in 1980. Flow denies the charges.

In addition, Flow's earnings have been diluted by its acquisition of Worthington Diagnostics for $60 million earlier this year.