Two of the nation's major banks, Chase Manhattan and Manufacturers Hanover Trust, boosted their prime lending rates to 17 1/2 percent from 17 percent today, the first increase in that key rate since late last year.

Chase Manhattan, the nation's third-largest, said it boosted its prime rate to reflect rising interest rates in the open market, where banks borrow much of the funds they then loan to their customers.

The rest of the nation's major banks did not follow the lead of Chase and Manufacturers today but analysts expect most banks to raise their prime rates to 17 1/2 percent soon and think short-term interest rates will continue to rise for another couple of weeks as businesses increase their demand for funds.

Late today the Federal Reserve Board, the nation's central bank, reported that business loans last week rose $2.2 billion and that loans by the giant New York banks climbed $900 million. (tables on Page D14)

That heavy demand for funds on the part of businesses "explains the pressures on money market rates" over the last two weeks, according to William Sullivan, vice president of the Bank of New York. When demand for funds rises, interest rates usually increase, as well.

The Federal Reserve, which could have injected lendable funds into the banking system during the last few weeks, did not. As a result, the so-called federal funds rate -- which is the interest banks charge each other for overnight loans of excessive reserves -- rose from about 13 1/2 percent to 15 1/2 percent, although the rate closed at about 15 percent today.

Analysts said it now appears that the central bank wants to keep the federal funds rate at about 15 1/2 percent to hold down the growth of business loans and the money supply. The growth of the money supply -- essentially checking accounts and currency in circulation -- is considered a key determinant of inflation.

The Federal Reserve announced today that during the week ended April 1 the money supply climbed $3.2 billion.

Many analysts thought the central bank had blessed the decline in the federal funds rate several weeks ago. But minutes of its policy-making Open Market Committee released last week showed that the central bank wanted to keep a tighter monetary policy than the 13 1/2 percent federal funds rate indicated.

Not only did the federal funds rate rise, but the whole spectrum of short-term interest rates in the so-called open market has increased sharply during the last two weeks. For example, the rate on 90-day certificates of deposit issued by big banks rose about 150 basis points (a basis point is one one-hundredth of a percentage point) and closed today at 15.15 percent.

Late today the Federal Housing Administration and the Veterans Administration announced that they had increased their basic mortgage rate from 14 percent to 14 1/2 percent to reflect rising interest rates.