Interest rates rose again in New York yesterday, fueling speculation that banks soon will increase their key prime lending rate, which is now 10 1/2 percent.

Analysts attributed the continued rise in money market rates this week to a further tightening of credit by the Federal Reserve Board and to market fears that a clash is likely between rising demands for private sector credit and large federal budget deficits.

The key federal funds rate climbed as high as 9 7/8 percent at one point yesterday and traded in the 9 3/4 to 9 7/8 percent range, higher than it has in recent days.

"I . . . think the Fed has started another round of tightening . . . a very small tightening," commented financial economist Mark Wanshel of Crocker Bank.

It "seems reasonable that the Fed should tighten," said Elliott Platt of Donaldson, Lufkin and Jenrette in New York, explaining that the economy apparently is growing strongly and that the money supply is likely to continue to exceed its Federal Reserve targets in the near term.

Platt and other analysts suggest that banks soon will be forced to raise their prime rate, but have considerable reluctance to take such an unpopular step. The major banks particularly are wary of raising rates while Congress still is considering the controversial bill to increase resources of the International Monetary Fund, one New York financier said yesterday. The bill has been attacked by some in Congress as a bailout for big banks that have made loans overseas to nations that now cannot repay on time.

The delay in raising the prime "can only be a temporary phenomenon," said the financier, who asked that his name not be used. Platt pointed out that, with rates on three-month bank certificates of deposits as high as 10 percent, the spread between the cost of funds to the banks and the interest they are charging on loans is "pretty tight."

The level of money market rates "would indicate that, even today," the prime should be at 11 1/2 percent--a full percentage point above the current rate, Wanshel said. Crocker Bank expects a further firming of money market rates in coming weeks, he added.

New York economist Alan Greenspan, an adviser to President Reagan and former chairman of the Council of Economic Advisers under President Ford, commented that "now is the classic time in the business cycle when the Fed should be tightening." The forces driving the economy are not particularly sensitive to interest rates, so an increase in rates would not damage the recovery, he said.