Chase Manhattan Bank sparked a new round of prime rate reductions yesterday by slashing its rate one full percentage point to 13 percent -- the lowest level since last September.

Chase, the nation's third-largest commercial bank, previously had been quoting the prevailing rate of 14 percent, adopted industrywide last week.

"The cost to the bank of the funds it borrows and in turn relends have continued to come down, and therefore . . . we feel 13 percent is the appropriate rate at this time," a Chase spokesman said.

The latest round of interest-rate cuts came as Treasury Secretary G. William Miller indicated the Carter administration may dismantle its credit controls program within a few months. Speaking at a banking conference in New Orleans, Miller said "my own feeling is that in the coming next few months it will be dismantled."

Miller cautioned, however, that President Carter hasn't commited himself to ending the controls program.

Following Chase's lead were Morgan Guaranty Trust Co. of New York the country's fifth-largest bank, and No. 13, Marine Midland Bank of Buffalo, N.Y. A number of smaller banks, including Manufacturers Bank of Los Angeles, also moved to 13 percent.

Meanwhile, the vice chairman off Manufacturers Haover Trust Co. predicted the prime rate would fall to between 10 and 11 percent by the end of the year.

John R. Torell III, in a meeting with reporters at the bank's New York headquarters, said he expects corporate loan demand to be flat for the rest of 1980, which will bring added pressures for further prime rate reductions. Manufacturers Hanover, however, didn't reduce its rate yesterday from 14 percent.

The last time the prime was 13 percent was Sept. 20, shortly before the Federal Reserve Board initiated the first in a series of credit-tightening measures that spurred an unprecedented upward spiral in the prime rate.

The prime is the base rate that banks charge on short-term loans to their most creditworthy corporate customers, while loans to most other businesses are set one or more percentage points above the prime.

The prime doesn't apply to consumer loans such as auto or home mortgage loans, but it is considered a key barometer of trends in all kinds of interest rates. When the prime changes, other rates -- including consumer loan rates -- usually follow.

Since the prime peaked at 20 percent in early April, banks have been lowering their rates as the emerging recession prompted businesses to cut back on borrowing and open-market interest rates plunged. When those rates fall, the banks' cost of lending does, too, because many of the funds they lend are acquired in the money markets.

Banks, for example, will be paying 8.415 percent interest on six-month money market certificates issued today and had been paying as little as 7.753 percent on certificates issued earlier. Those rates compare with a peak of 15.7 percent reached in late March.

The six-month savings certificates, issued in minimum amounts of $10,000, are a significant source of lending and investing funds for banks.

Banks also are paying less to borrow money from other banks. The interest rate on federal funds -- which are uncommitted reserves that banks lend one another on an overnight basis -- has hovered between 10.5 percent and 11.5 percent this week, down from a peak of about 18 percent in March.