Interest costs to the government, as measured by weekly Treasury auctions of 13-week and 26-week bills, rose for the sixth consecutive week yesterday to the highest levels in five months.

The average discount rate on 13-week bills rose to 14.74 percent from 14.099 percent a week earlier. The investment rate, or equivalent coupon-issue yield, was 15.52 percent compared with 14.82 percent for the previous bill auction on Feb. 8. It was the highest since Sept. 4, when the discount rate was 15.611 percent.

For 26-week bills, the discount rate was up to 14.36 percent from 13.933 percent. Equivalent coupon-issue yields rose to 15.7 percent from 15.2 percent a week ago. The discount was the highest since 14.932 percent on Sept. 30. The Treasury sold $5 billion each of the 13-week and 26-week bills.

Officials of the Reagan administration have forecast a 1982 average yield of 11.7 percent for three-month bills compared with the 14.1 percent average of last year. But yields have steadily risen to the current level from the 11.658 percent of Jan. 4, thereby increasing the cost of financing the federal budget deficit.

Beginning today, banks and savings and loans may pay as much as 14.61 percent interest on $10,000-minimum, six-month money market certificates, up from the previous 14.183 percent. Also today, S&Ls may pay as much as 15.05 percent and commercial banks as much as 14.8 percent on 2 1/2-year "small-saver" certificates, up from the ceilings of 14.55 percent and 14.3 percent for the previous two weeks.

The Treasury also announced yesterday that it will sell $3.25 billion of five-year, two-month notes a week from today to raise fresh cash. The notes will be in minimum denominations of $1,000, and tenders from investors must be received by 1:30 p.m. on Feb. 24 at the Treasury here or Federal Reserve banks and branches, including Richmond and Baltimore. The Treasury will sell $5.25 billion of two-year notes today (minimum $10,000).

Separately, the Federal Home Loan Banks announced a $1.7 billion debt offering for Thursday: $900 million maturing Dec. 27, 1983; $500 million maturing in four years; and $300 million maturing in seven years. Rates will be announced today.