The Senate Finance Committee hinted yesterday it probably will weaken the House-passed version of President Carter's "windfall profits" tax on oil, but there was no immediate indication just how far it will go.

In an opening day of hearings on the measure, panel members were almost unanimous in expressing concern that too stiff a "windfall tax" might inhibit additional oil production, implying they plan to weaken the House bill.

However, the senators offered no specific proposals for paring the tax enacted by the House, and there were no calls for a sweeping "plowback" provision that would exempt any new revenues the oil compaines re-in-vested.

Sen. Hohn Heinz III (R-Pa.) told administration officials at one point that the measure "appears to be in pretty good shape" In the comittee. I nevertheless, most observers still believe the panel will weaken the house bill.

The response came as the administration generally endorsed the House version of the legislation, but asked the Finance Committee to make some changes that would stiffen some provisions that were diluted on the floor.

Treasury Secretary W. Michael Blumenthal called on the committee to make permanent a portion of the tax to be imposed on newly discovered oil, which the House voted to phase out by 1990.

He also called for a toughening of the measure's treatment of "tertiary" oil -- petroleum that is more difficult to flush from the ground -- and for elimination of a special exemption for oil wells owned by states.

Carter originally proposed a relatively mild "windfall " tax that would impose a 50 percent levy on a small portion of the additional revenues that the oil companies are expected to receive from his decision to lift price controls.

The House Ways and Means Committee voted a far tougher tax, approving a 70 percent tax rate and other revenue-raising changes. But oilstate lawmakers succeeded in reducing this to 60 percent on the floor.

Under questioning by committee members yesterday, Blumenthal attempted to fend off conservatives' complaints that a stiffer tax might inhibit production by portraying the measure as a necessary compliment to oil price decontrol.

"If we did not have this tax," the secretary told the panel, "certainly we would run the risk that controls would be reinstituted." At another point, he said decontrol was "absolutely essential, whatever else is done."

Blumenthal also assured the panel the administration would not mind if Congress earmarked some of the measure's new revenues for loan-guarantees and tax credits to industry to cover the cost of new exploration.

The White House has proposed using the new "windfall" tax monies -- along with extra revenues from added income taxes the oil companies will have to pay -- for a new energy trust fund to finance new exploration.

The House Ways and Means Committee decided to sparate that portion of the package to help speed the tax bill through the House. However, some senators want to consider the two together.

The changes the administration proposed in the House version of the bill were, generally speaking, relatively modest. The Treasury estimated they would add a net $431 million to the measure's tax bite over five years.

However, that figure masks the impact of the proposal to toughen the House bill's treatment of tertiary oil, which would bring in an extra $898 million in new revenues in 1984 alone.

Blumenthal also asked the panel to ease the tax on already-discovered Alaskan oil. Carter proposed originally exempting Alaskan oil entirely, but the House voted to allow only new Alaskan oil to excape any levy.

The administration also provides new estimates of the monies it expects to receive for the energy trust fund -- both from the "windfall" tax and additional oil-company income taxes -- showing a sizable fund it prices rise slightly.