The coal industry yesterday rejected an independent company's tentative agreement with the United Mine Workers as a model for settling the nation's 78-day coal strike. But the industry offered to resume talks, and the union accepted.

Negotiations resumed shortly afterward, with top industry officials and later union bargainers shuttling in and out of the Labor Department for separate meetings with Labor Secretary Ray Marshall. Marshall sent the bargainers home by early evening, saying he would stay in contact by telephone with both sides.

The White House said it was "somewhat encouraged" by the bargaining resumption but not sure the talks would be productive.

The new round of talks came as the White House consulted with congressional leaders about direct governmental intervention to end the walkout -- but once again stopped short of acting in hopes that a voluntary agreement could be worked out.

"I think the president must do whatever he needs to do," said Senate Republican Leader Howard H. Baker Jr. (Tenn.) in lending an aura of bipartisanship to the Democratic administration's grouping quest for a governmental solution to the increasingly disruptive strike.

But Republican National Chairman Bill Brock sang a different song, accusing Carter of "waffling and buckpassing" and calling on him to "display the leadership and fortitude he promised the American people when he was campaigning for office" by appointing a board of inquiry under the Taft-Hartley Act.

A board of inquiry could lead to an 80-day back-to-work order from the courts, a course that the administration is reluctant to pursue because of widespread predictions that the 160,000 strikers would defy such an injunction.

Congressional and administration sources indicated that temporary government seizure of the mines was the preferred course of action, but some Capitol Hill leaders have warned that congressional authorization, which is required for a mine takeover, could be controversial and disruptive to deliberations on the Panama Canal treaties in the Senate.

Presidential press secretary Jody Powell reiterated yesterday that a decision will "have to be made" this week.

Faced with a seemingly intractable stalemate between the UMW and the Bituminous Coal Operators Association, the industry's major bargaining group, the administration pinned its dwindling hopes for a negotiated end to the strike on a tentative agreement reached over the weekend between the union and the Pittsburg and Midway Coal Mining Co.

P&M, a Gulf Oil Co. subsidiary, is not a member of the 130-company BCOA, but government and union officials hoped the P&M pact would escalate pressure on the industry association to improve its "final" offer of last Saturday.

The UMW's bargaining council unanimously rejected the BCOA offer but late Monday approved the P&M settement, raising hopes -- however slim in light of the industry's previous position -- that BCOA might accept the P&M pact.

After meeting several hours on the issue, top BCOA leaders said that "certain collective bargaining matters which we negotiated in good faith . . . were not dealt with adequately" in the P&M settlement.

This was an apparent reference to wildcat strike controls, production incentives and major changes in union benefit plans that were proposed by BCOA and dropped or modified by P&M. The two contracts are not far apart on economics, which would raise miners' compensation by nearly 37 percent over three years.

BCOA's response came in a letter to Gov. Jay Rockefeller of West Virginia and governors of three other coal-producing states who appealed earlier to the association to resume talks.