"I think they could go up just as well as down," a New York economist said yesterday, summing up the deep uncertainty about the future course of interest rates that continues to trouble financial markets.

A drop in rates last week, coupled with better-than-expected money supply figures, led many in the markets to hope that the long-awaited break in interest rates was about to happen.

Yesterday, yields on Treasury bills fell sharply in the weekly auction to their lowest levels since May.

Ironically, this good cheer comes on the heels of administration predictions that the next rate movement probably would be upward rather than downward. Treasury Secretary Donald T. Regan and Chairman of the Council of Economic Advisers Murray Weidenbaum recently have said rates are likely to climb.

Henry Kaufman, chief economist for Salomon Brothers investment banking house in New York, yesterday repeated his gloomy interest-rate predictions, saying in a quarterly report that "both short- and long-term interest rates will rise further in the second half of 1982, with long-term interest rates reaching their 1981 highs, while short-term rates will probably fall shy of their previous peaks." That would put them in the 17 percent to 20 percent range.

The pessimists may be proved right. Some interest rates moved up slightly yesterday from their lows on Friday, and some analysts believe that last week's market rally may have been an overreaction. "The rally, I think, is fading at the moment," said Elliot Platt of Donaldson, Lufkin, Jenrette yesterday, although the upward momentum continued.

One trigger for last week's optimism was a widespread belief in the market that the Federal Reserve was easing its policy by supplying more reserves to the banking system and encouraging interest rates to drop. However, few insiders believe that the Fed's actions reflected any easing in its monetary objectives. There have been no indications that it plans to raise its monetary targets.

Rather, with a $9 billion decline in the money supply in the last three weeks of June, the Federal Reserve was able to supply more funds to the system without threatening its monetary targets. "I think it was a very monetarist reaction," Platt said.

Others believe that the Fed was keen to make its presence felt to reassure financiers after the collapse of Penn Square National Bank in Oklahoma.

Neither of these reasons for action implies a change in the Fed's basic policy stance. Given the evident weakness in the economy, the Federal Reserve probably would not be sorry to see rates fall, one analyst said. But "I doubt if the Fed is going to lead interest rates down. It would be happy to follow," another remarked.

Dealers who predicted a change in Fed policy were "grasping at straws," he said. When the Fed was then absent from the market yesterday, people were "a bit jittery," he went on.

One major reason for the uncertainty over where rates are now headed is that no one is quite sure why they are still so high, and therefore what might trigger a fall. While most analysts expected rates to fall during the recession, they have remained remarkably steady.

Another major uncertainty concerns the money supply. For weeks analysts have predicted a huge money bulge in the first week of July as increased Social Security benefits are deposited in bank accounts. This rise, if it happened, will be reported on Friday. If it is as large as $7 billion, as several analysts believe, then M1 will be pushed right back up to the top of the Fed's target growth range, after dipping into the bottom half of the range in the previous week.

For as long as M1--which measures currency in circulation and all checking accounts--is perilously close to the top of its target, or outside it as it has been for almost all of this year, the Fed is unlikely to go far toward easing credit conditions. Although rates have stayed higher than Fed officials expected, given their targets, they have not attempted to push them down.

Kaufman blamed his poor prognosis for rates on the large overhang of Treasury borrowing. He said that the Treasury may have to raise as much as $95 billion net in the second half of this year compared with only $58 billion in the same period last year. The market is "not capable of accommodating these needs without higher interest rates and without increasng the financial vulnerability of some credit demanders in the private sector," he said yesterday.