Federal Reserve Board Chairman Paul A. Volcker yesterday appealed for "breathing room" to solve what he called the "untenable" and "chaotic" situation gripping the financial industry because of deregulation.

Volcker repeated his call for a temporary ban on the acquisition of banks and thrift institutions by non-bank companies and on expansion of non-banking activities by state-chartered banks until Congress can work out a solution.

Senate Banking Committee Chairman Jake Garn (R-Utah) rejected a moratorium, saying such a tactic would be sure to delay any legislation. He conceded no major legislation is likely to pass this year anyway.

Volcker endorsed the administration's proposal to let banks, through holding companies, expand into insurance, mutual funds, real-estate brokerage, and underwriting revenue bonds.

To cut down the risk for banks in new fields and to avoid potential concentration, Volcker called for limitations, such as forbiding the largest banks from purchasing the largest insurance companies and vice versa. Volcker's testimony occurred on the same day that Prudential, the country's largest insurer, announced that it had hired Charles E. Lord, vice chairman of the Export-Import Bank, to coordinate its expansion into banking.

He also urged that state-chartered banks that have federal insurance not be allowed to pursue activities that are prohibited for federally chartered banks. South Dakota is the most frequently cited example of a state that has eased regulation, allowing its banks to write insurance. Citicorp and Bank of America have recently entered South Dakota for that purpose.

While advocating an end to barriers against interstate branching, Volcker suggested steps that could be taken to prevent the realization of fears of small banks--and the politicians representing them--that big banks will drive them out of business.

Making his debut as chairman of the Federal Home Loan Bank Board, Edwin J. Gray warned the committee that thrift institutions are still in a "fragile recovery stage. While spreads on assets began to move back into the black during the first part of 1983, today's interest rate environment is causing many thrifts to slip back into the red."

He cautioned that the legislation endorsed by the Federal Reserve and Treasury could limit savings and loans' powers and make them less attractive to investors. Such a change would threaten the conversion of mutual S&Ls to stock associations, a process that has brought more than $2 billion in new capital into the industry this year.