A small but influential St. Louis bank cut its prime leading rate by two percentage points to 13 percent today, building pressure for a further decline in interest rates.

More major banks, meanwhile, lowered their prime rate to 14 percent, following reductions first made Tuesday by several of the nation's largest banks.

The Southwest Bank of St. Louis, frequently a leader in setting prime lending rate levels, undercut the 14 percent mark, with its drop to 13 percent, but the move was not followed immediately by any major banks.

Today's action continues a sharp decline in the prime rate since a record 20 percent level was reached in April. The latest retreat brings the St. Louis bank's prime rate down to the discount rate, the charge on loans to banks by the Federal Reserve Board.

Following suit to the 14 percent rate today were Chemical Bank, Bank of New York and National Bank of Detroit. Chemical had been charging a 15 percent prime rate. While the others previously posted a 14 1/2 percent rate.

The prime the interest rate charged a bank's most creditworthy business customers doesn't affect consumers but is reflective of trends in the money market that eventually filter down into consumer rates.