Pressures are building for an increase in the prime lending rate charged by the nation's major commercial banks despite the continuing recession.

The banks' cost of funds has been rising as short-term interest rates continued an upward march begun in later November. Most banks currently charge a prime rate of 15 3/4 percent.

Long-term rates have also risen since then, in some cases by nearly two full percentage points.

At its monthly auction yesterday, the Treasury Department sold $5.25 billion of one-year bills at an average annual return of 13.143 percent, up from 12.501 percent last month. Treasury said the average investment yield on the bills was 15.37 percent. This means that the annual return on All-Savers certificates issued by banks and thrift institutions starting Sunday will be 10.76 percent, up from the current 10.16 percent.

Financial analysts, and Washington policymakers, are hoping the weekly money supply figures to be released this afternoon by the Federal Reserve will give a strong clue whether the recent sharp increase in the money supply is an aberration, or whether the Fed will have to take new action to slow its unexpected and puzzling growth. Such action would mean still higher interest rates in the near term and probably prolong the recession, analysts said.

Rep. James Jones (D-Okla.), chairman of the House Budget Committee, warned that huge federal budget deficits will keep long-term interest rates "at very high levels" throughout 1982. In a speech to a group of state and local finance officers, Jones described the long-term bond market as being "virtually dead" for the remainder of the year.

Meanwhile, administration officials remained sharply split over whether they think the Federal Reserve is properly managing monetary policy. President Reagan at his press conference this week said uncertainty over Fed policy was delaying needed investment by business.

Treasury Secretary Donald T. Regan also criticized the Fed in two speeches this week for not achieving more rapid and less erratic money supply growth during 1981. "We had hoped for a gradual reduction in money supply growth, from the 8 to 9 percent rates in the Carter years, to a steady 7 percent for 1981, a steady 6 percent for 1982 and so on down to a steady 4 percent for 1984 and beyond," he said, adding that "M1-B growth fell to 4.6 percent for 1981, in an unsteady fashion."

A 6 percent growth of M-1 in 1982--the "B" was dropped as of the first of the year but without change in the measure's composition, which includes currency in circulation and checking deposits at financial institutions--would exceed the Federal Reserve's target range of 2 1/2 percent to 5 1/2 percent. It would be 2 percentage points above the mid-point of the range.

Treasury officials said yesterday that Regan was not suggesting a change in the Fed targets for this year, but rather was describing what the administration had hoped when it first took office that the money supply growth path would be.

Other sources familiar with the drafting of the administration's initial statements on monetary policy suggested that the numbers cited by Regan originally referred not to the money supply but to the monetary base, another measure that includes currency and reserves at financial institutions but not checking deposits. It was assumed in the drafting, the sources said, that money supply growth would be about 1 percentage point less than the growth of the monetary base.

Other analysts noted that M1-B growth in the final two years of the Carter administration was 7.5 percent and 7.3 percent respectively. Thus a 7 percent growth rate for 1981 would have represented little if any of the slowdown in money growth that administration economists maintained was needed to reduce inflation.

Separately, the Federal Reserve said that M1-B growth from the fourth quarter of 1980 to the fourth quarter of 1981, the period over which it specifies its annual targets, was 5 percent rather than 4.6 percent. Treasury officials said the 4.6 percent was calculated in a different way.

Administration economists outside of Treasury are not nearly as critical as Reagan has been. "I think the Fed should just stick to their course," one said yesterday. "They've been on track for the last year.