Chemical Bank of New York, the nation's sixth largest bank, raised its prime lending rate to 13 1/4 percent yesterday, the sixth such increase to set a record level since late July.

The latest peak in the prime -- the rate banks charge their most-credit worthy customers -- could be surpassed before the week is out because of indications that the Federal Reserve still is pushing up interest rates, some money market analysts warned.

The surge in interest rates also has hit home mortgages but it hasn't choked off housing construction. The Commerce Department reported yesterday that housing starts in August were at a 1.783 million seasonally adjusted annual rate, only 8,000 below the level for July.

Separately, Commerce also reported that the gross national product fell in the second quarter of this year at a 2.3 percent annual rate instead of the 2.4 percent rate reported last month. However, prices, as measured by the GNP deflator, rose a bit more rapidly, at a 9.3 percent rate compared with the 9.2 percent rate estimated earlier.

Treasury Secretary G. William Miller said in a speech to the National Conference of State Legislatures that despite the increases in interest rates, "I don't expect, and I don't see conditions for, a credit crunch."

Miller said he thinks credit will remain available to most qualified borrowers, but that the higher interest rates would discourage some borrowing.

The secretary said a recession began with the drop in GNP in the second quarter, but that the third quarter "won't be that weak . . . . It (GNP) may be around zero."

The third-quarter strength is due to an accumulation of business inventories, he said. An "inventory adjustment" will mean a renewed decline in the fourth quarter, Miller added.

"The recession will be moderate, and it will go on for about four quarters," he continued. The economy will "begin to come out of the recession in the second quarter of next year as the result of a "normal self-healing process," he predicted.

Meanwhile, presidential Press Secretary Jody Powell said although the administration expects some "positive" news on inflation by the end of the year, the country will face economic problems "into next year."

Any improvement in inflation "won't be dramatic," he cautioned. "If the question is whether our economic problems are going to be solved any time soon, the answer is, no," Powell told reporters.

Yesterday the Federal Reserve allowed the so-called federal funds rate to rise from 11 3/8 percent to 11 1/2 percent as it continued its effort to get the recent rapid expansion of the money supply under control and to contain inflation.

The federal funds rate is the interest rate banks charge each other for loans, often on an overnight basis. The Federal Reserve watches it closely as an indicator of the amount of funds available to commercial banks with which they can make loans to the public. The Fed adds or subtracts funds in the banks by selling or buying government securities.

In the revisions of the second-quarter GNP figures, the Commerce Department also said that corporate profits from current production decreased $2.3 billion to a seasonally adjusted annual rate of $176.6 billion. That is $1.1 billion higher than the preliminary estimate issued last month.

Housing construction has continued to surprise many forecasters who had expected savers, attracted by higher returns elsewhere, to withdraw funds from the thrift institutions that make more home mortgage loans. Lenders have found other sources of funds when savings inflows have slowed down and have kept mortgage commitments high, according to Kenneth Biederman, chief economist for the Federal Home Loan Bank Board.