Federal Reserve Board chairman Arthur F. Burns said yesterday the nation's banking system "has past well beyond the worst of its recent difficulties and is in fact regaining strength steadily."

Burns also told the Senate Banking Committee that his agency is working with congressional and bank regulatory officials to develop legislation that would permit banks nationwide to pay interest on checking accounts.

The so-called NOW accounts, for "negotiable orders of withdrawal," currently are confiined primarily to New England. Burns said interest-bearing checking accounts should be available to individuals but not to corporations or non-profit organizations.

Separately, Federal Deposit Insurance Corp. chairman Robert E. Barnett said the U.S. banking industry is in "reasonably sound shape" and getting stronger, even though the number of problem banks is close to its highest level in history.

Barnett told the Financial Analysts Federation that banks in various problem categories stands at 384 compared with a 1976 peak of 385, the highest number since 1948. "I don't find that number particularly significant," said Barnett, who is scheduled to testify today before the Senate committee.

In his testimony yesterday, Burns proposed a ceiling on the interest paid on NOW accounts that should be somewhat lower than the 5 per cent paid in New England. He said it will take about two years for the nation's banks to develop the necessary arrangements including service charges, advertising and computer changeovers.

He also recommended that after a few years of participating in NOW accounts, the recommended interest ceiling rate should be removed.

On another subject, Burns said the Organization of Petroleum Exporting (OPEC) countries provoked economic war against the industrial world when they raised oil prices. He said the industrial world didn't respond and that this situation is at least partially responsible for current world wide inflationary pressures.

Burns noted that U.S. banks currently hold about $45 billion in OPEC deposits and said that the system is not capable of handling such massive surplus funds. He said the OPEC nations will have to become more active in the financial world and become bankers in order to assist underdeveloped countries whose economic problems they themselves have exacerbated.

Although Burns did reveal some problems that exist within the domestic banking system, he said analysis by the Fed, "leads to the conclusion that the nation's banking system has past well beyond the worst of its recent difficulties . . ."

Burns noted there has been a greater sense of caution on the part of bankers in extending credit. However, they have not adopted a stagnant policy and loans continue strong, he asserted.

The chairman noted that between the end of 1974 and the end of 1976 commercial banks added enormously to the U.S. government securities holdings, in all about $47 billion. He said this emphasis on liquid assets has strengthened the general quality of bank assest positions.

Burns said the "so-called problem banks represent only a small percentage of the total number of commercial banks in the U.S. - less than 5 per cent even at the worst readings of recent years."

One area of concern with respect to the soundness of the banking system is the continued attrition in Federal Reserve membership, he testified.

Burns told the committee that in 1976, some 46 banks gave up membership and 8 banks left the system as a result of merger with non-members. He said that over the past eight years 427 banks have dropped their memberships and another 91 have left because of mergers.

Burns said these banks have left mainly because of the "high cost of the non-interest earning reserves that they are required to hold as members of the Federal Reserve."

They chairman warned that unless this trend to non-membership is reversed. The soundness of the banking system will be jeopardized because so many banks will not have direct access to Federal Reserve discounts.

FDIC chairman Barnett said the number of banks in serious problem categories has decliend substantially from a high of 128 and that the number of banks that were not on FDIC throughout this period.