As banks continue to offer more services and with interest rates for savers expected to rise significantly in the coming years, consumers will be paying more for bank services, Riggs National Bank President Daniel Callahan said yesterday.

Callahan, addressing the Washington Society of Investment Analysts, also said increases in check processing volume will "cause the processing costs to escalate sharply."

Callahan also predicted the prime rate would decline slightly during the balance of 1979 and would reach a low of 11.5 percent or 12 percent by the end of next year.

As of yesterday, most banks were operating with a 15 3/4 percent prime rate, although some banks had reduced the rate to 15 1/2 percent and others to 15 1/4 percent.

Callahan said that no matter how legislative proposals to deregulate banking turn out, interest rate ceilings eventually will be phased out. A controversial bill passed recently by the Senate would phase out limits on interest rates over a 10-year period.

"This bill alone, if it becomes law, will have significant impact on the whole financial industry, its pricing and, therefore, its profits,' he said.

Callahan said that lifting the federally imposed ceiling would intensify competition for savers' dollars, ultimately driving up the costs consumers pay for banking services.

Callahan also expressed his concern that foreign banks, which have been bringing representatives to Washington, might open actual business offices here.

If that were to occur, he said, embassies might pull their accounts, from Riggs and move into banks representing their nations. Callahan said the embassy accounts were "very meaningful" to Riggs and that he "could see an erosion if any particular" foreign bank opened an operating branch here.

"Foreign banks should continue their penetration of the U.S. market by both expanding existing operations, as well as acquisition of domestic banking and other financial institutions," Callahan said. "A legitimate concern is still the competitive advantage enjoyed by overseas banks in the United States." Foreign banks are not restricted in their branching abilities.

Nevertheless, Callahan said Riggs has experienced "impressive growth" in recent years, despite statistics indicating nationwide cuts in consumer savings.

For example, Callahan noted that Riggs' interest margin has risen from $58 million in 1975 to $74 million in 1978. That margin also is up 21 percent for the first nine months of this year, over the same period last year. p