The nation's top federal bank regulators said today that the number of bank failures is rising steadily and will continue to rise at a record rate next year as the recession and a legacy of high interest rates take their toll on financial institutions.

Bank failures, already at a post-World War II record, are likely to increase in 1983 along with the number of problem loans. Problem loans are those that are not being paid off on schedule.

C.T. Conover, comptroller of the Currency, and William Isaac, chairman of the Federal Deposit Insurance Corp., told the annual meeting of the American Bankers Association, however, that these developments were normal during a recession and its aftermath. In separate speeches, the two regulators assured their ABA audience that the U.S. banking system is sound despite the increasing number of companies and foreign governments that are having difficulties repaying their loans.

The 35 commercial and mutual savings bank failures this year are more than double the previous one-year record of 16 set in the 1976 recession. Normally, five to 10 banks fail each year. The number of banks on the special problem list maintained by regulators is lower this year than it was in 1976. There are 320 banks on the list this year, compared with 385 banks in 1976.

Bad loans -- those written off as uncollectable -- are running at an annual rate of about $4 billion, or 0.35 percent of the total loans made by the nation's 14,600 banks. In 1975 and 1976, bad loans accounted for 0.56 percent of total loans.

Willard C. Butcher, chairman of Chase Manhattan Bank, the nation's third biggest, said that banks are in better shape now than they were in 1975 and 1976, even though the current recession is much worse than the earlier one. In an interview with reporters, he said this is because bankers have learned from their mistakes.

Neither Conover nor Isaac would predict how many banks likely will be added to the 320 already on the problem list. At the start of 1981, there were 220 banks on the list.

Both Conover and Isaac said the economic problems confronting the nation's banks would be compounded by the increasing move to deregulate the industry and growing competition from other financial institutions.

Savings and loans associations, which have suffered far more in recent years than commercial banks, have been granted expanded loan-making powers. Deposit costs at banks and S&Ls will rise as consumers begin to take advantage of new money market fund type accounts that regulators are expected to approve this week. Competition from non-bank financial institutions, such as brokerage houses, will continue to grow as well, the regulators said.

Isaac said that as federal regulation of banks eases, regulators are looking for ways to substitute "market discipline" for federal oversight.

Next year, despite resistance from many bankers, the federal agencies will make public the level of problem loans as well as other heretofore secret data, at each of the nation's banks. The regulators think the increased disclosure will permit depositors to make more intelligent decisions about the banks with which they deal.

Isaac said he thinks a way should be found to make big depositors share more of the risks of a bank failure even when -- as usually happens -- the FDIC finds a merger partner for the bank. By forcing big depositors into the role of risk takers, Isaac said they will be more careful and will impose a new level of discipline on bankers. He said a system of private insurance for deposits that exceed federal insurance limits might develop and private insurers would also be tough on bank practices.

Major depositors at the failed Penn Square National Bank stand to lose 20 percent or more of their deposits over $100,000 -- the current federal insurance ceiling. But had Penn Square been merged with another bank, a tactic regulators said was impossible in that case, all deposits would have been made whole.