The government is investigating complaints about United Mine Workers' health benefits but will not intervene to end a stubborn, two-month-old wildcat strike over benefit cutbacks, Labor Secretary Ray Marshall said yesterday.

Marshall's statement appeared aimed at convincing an estimated 85,000 strikers to return to work, while keeping the government from getting mired in the quicksand of union infighting and collective bargaining in the Appalachian coalfields.

Although the striking miners had demanded a government investigation as a major condition of returning to work, Marshall held out little hope that it would solve the financial problems that forced the benefit cuts.

"That is not our responsibility and I think it would be irresponsible to raise expectations in this area," he said in a prepared statement before a press conference.

As many as 85,000 UMW miners - nearly half the union's active members - have been on strike since laste June to protest a cut in benefits that requires miners to pay up to $500 a year for previously free medical care. Subsidies to coalfield clinics have also been eliminated, threatening some of them with bankruptcy.

"Since the (UMW) Health and Welfare Fund derives its revenues from the production of coal, these work stoppages are only making a bad situation worse," Marshall said in urging the strikers to go back to work.

The strike has virtually shut down coal mining in West Virginia and sharply curtailed mining in several other states. In a dkind of revolving door, some strikers were reported returning to work yesterday as others were going out.

Marshall estimated the number of strikers at 50,000 to 70,000, although a UMW source said at least 85,000 were on strike yesterday. The union has about 180,000 working members, who produce a little more than half the nation's coal.

The National Coal Association warned earlier this month that the strikes will cause production this year to drop 33 million tons short of demand, forcing some depletion of stockpiles and possibly local shortage. Coal production is now estimated at 665 million tons for the year, the association said.

It was unclear yesterday whether Marshall's announcement of the Labor Department probe would spark a back-to-work movement. Previous efforts by union leaders to end the walkout, including a televised appeal by UMW President Arnold Miller last weekend, have failed.

Marshall, who met earlier this week with Miller and Joseph P. Brennan, president of the Bituminous Coal Operators Association, urged at his press conference that bargaining for a new contract begin soon. The current contract expires Dec. 6, giving rise to speculation that the wildcats will escalate into a full-fledged nationwide coal strike by the end of the year.

A bid by West Virginia Gov. Jay Rockefeller to open the bargaining in Charleston on MOnday was rejected yesterday by the BCOA. The UMW Executive Board plans a meeting Monday in Charleston on the strike issue, prompted by a demand from District 17, the union's largest district and most militant strike supporter.

In discussing the department's role, Marshall reiterated his belief that it is "not proper or effective for the Labor Department to become involved in collective bargaining negotiations." But he said it would investigate all allegations of irregularities involving health and pension funds, as required by law. "We have no evidence that there was anything improper about the decision to reduce health and welfare benefits," he emphasized.

Assistant Labor Secretary Francis X. Burkhardt said complaints received thus far center on two point: Whether nonmenbers hold union health cards and whether some operators are delinquent in their contributions to the funds.