The Reagan adminitration appeared to reverse its commitment to building up the nation's strategic petroleum reserve yesterday when it failed to object to proposals to cut spending sharply for the stockpile in fiscal 1982.

Rapidly rebuilding the reserve (SPR) has had wide backing among Republicans, was endorsed by President Reagan during the campaign and was reaffirmed by Office of Management and Budget Director David Stockman during his conformation hearing, and in other testimony on Capitol Hill. The administration committed $3.8 billion to the reserve plan in fiscal 1982.

But when the Senate Budget Committee's reconciliation resolution recommended deleting $3 billion of that amount, Stockman told Energy Committee Chairman James McClure (R-Idaho) -- also a member of the Budget Committee -- that "his position was not totally negative," OMB spokesman Edwin L. Dale said.

He admitted that the White House position was further confused "by mixed signals" that were sent on Wednesday to Sen. Bill Bradley (D-N.J.), who plans to introduce an amendment to the budget resolution restoring the missing $3 billion. On Wednesday, White House aide David Swanson phoned the Bradley office of say the administration would support the Bradley bill.

But 10 minutes later, Swanson called again, on instructions from White House counsellor Ed Meese, to say that the White House could not take that position.

Late yesterday, in response to a query, Dale said that on Wednesday "the administration position was just plain mixed up. But the administration is now neutral; it has no position."

By "neutral," Dale meant that the administration, while sticking to it position that filling the SPR is a strategic necessity, now is willing to let Congress try for alternative financing. The Senate Budget Committee deletion of the $3 billion was predicated on the assumption that the SPR could be financed privately beginning next Jan. 1.

Budget Committee staff director Steve Bell said the committee was torn between "the very substantial savings in SPR that could give us a larger [budget reduction] number than the president sent up" and an awareness that shifting to private financing would be difficult.

Other Capitol Hill sources suggested that a compromise might yet be struck between the $3.8 billion and $800 million figures, although politicians, running the Budget Committee are frankly anxious to hang on to most of the difference to top the Reagan estimates.

Bradley and other strong supporters of the SPR doubt that private financing can be brought into effect quickly, if at all. The OMB originally decided to put $3.8 billion into the budget for the SPR only after Stockman had examined the possibility of selling oil bonds to raise the money and then rejected the plan, because such bonds would not reduce total governments borrowing needs in financial markets.

Before the OMB decided late yesterday to say that the government was neutral on the issue, an OMB official suggested that if the Budget Committee was justifying its stand on the prospect of shifting to some device such as oil bonds, the prospective saving would be "phony."

According to Capitol Hill sources, Stockman told McClure that the administration would return to supporting the $3.8 billion budget item only if the Budget Committee could come up with $3 billion worth of offseting reductions elsewhere in the budget.

A "Dear Colleague" letter sent Wednesday by Bradley, and Sens. Henry M. Jackson (D-Wash.), Bennett Johnson (D-La.) and Lowell Weicker Jr. (R-Conn.), charged that the Budget Committee action "has the potential to confirm and prolong our vulnerability to supply disruptions."

At the moment, the SPR totals 118 million barrels, enough at the present rate of imports to fill 24 days' needs if the flow of all oil from the Persian Gulf were halted, or 40 days if Saudi Arabia exports alone were halted. What frustrates supporters of the SPR is that the reserve supply in the past few months has been supplemented by at least 10,000 barrels a day, with no objections from the companies, and notably none from Saudi Arabia.

"They've just been looking the other way, and saying: 'Just don't tell us about it -- we don't want to know'," said a Hill source. "But if the budget only has $800 million, the program will grind to a halt just when it was getting going again."