Short-term interest rates continued to rise yesterday as financial markets continued to worry about the huge amount of debt the Treasury will have to issue in coming months.

The average discount yield on three-month Treasury bills at yesterday's weekly auction jumped to 13.269 percent, up from 12.588 last week and the highest level since March 29. The comparable rate on six-month bills rose to 13.419 percent from 13.031 percent the week before, reaching the highest level since Feb. 16.

The rates major banks paid on large certificates of deposit also continued to rise, hitting 15.45 percent. Since large CD's are a significant source of lendable funds for major banks, the increase could lead soon to a rise in the banks' prime lending rate, which is currently 16.5 percent, analysts said.

Reagan administration officials and many private economists are concerned that high interest rates will choke off the economic recovery expected for later this year. Both within the administration and at the Federal Reserve, key officials are hoping an upturn in sales will improve business cash flow, ease the demand for short-term credit and lead to lower interest rates.

But so far, financial markets seem more impressed by the certainty of Treasury borrowing and rates keep rising.

The results of the Treasury auction mean that the ceiling rate on six-month money market certificates at banks and thrift institutions will go up to 13.669 percent for the week starting today. The rate is set at one-quarter percentage point higher than the latest yield on six-month bills, or at the average of the last four auctions, whichever is higher.

The rate payable on the new 91-day savings certificate at thrift institutions will go up today from 12.588 percent to 13.269 percent. The rate at commercial banks is one-quarter percent lower.

The return, or investment rate, came to an average 14.6 percent on six-month bills and 13.92 percent on three-month bills.