The nation's top labor and industrial leaders, working with former Labor secretary John Dunlop, have formed a joint labor-management committee outside the government to try and deal with mutual problems facing their industries.

Formation of the group, which will have no formal ties with the government, comes as labor-relations experts fear possible major strikes aimed at the Reagan administration over proposed cuts in the budget.

The United Mine Workers union yesterday announced a two-day strike March 9 and 10 to protest proposed cuts in the federal black lung benefits program. A top labor-relations expert said there also were fears the budget cuts, if enacted, might trigger major strikes later this year against the U.S. Postal Service and the railroad industry.

The White House has proposed sharp cuts in the Postal Service budget as well as the budget for Conrail, the federally supported rail service in the Northeast. New contracts must be negotiated in all three areas this year, and some labor experts fear worker bitterness toward the Reagan administration could result in what would amount to strikes against the government.

Formation of the new Labor-Management Committee, which would be headed by AFL-CIO President Lane Kirkland and Exxon Chairman Clifton C. Garvin, is scheduled to be announced next Wednesday. Other management members of the committee will be Philip Hawley, president of Carter Hawley Hale Stores; John F. Welch, chairman of General Electric; Roger B. Smith, chairman of General Motors; Walter B. Wriston, chairman of Citicorp and Irving and Irving Shaprio, chairman of Du Pont.

Labor members, in addition to Kirkland, will be Thomas Donahue, AFL-CIO secretary-treasurer, Lloyd McBride, president of the United Steelworkers; John Lyons, president of the Ironworkers union; and Martin Ward, president of the Plumbers union. It was unclear whether the United Auto Workers and the Teamsters, the nation's two largest unions, would be represented on the committee.

Sources close to the new committee operation said the Reagan administration was not involved in the formation of the group.

The Reagan administration has expressed little interest in becoming involved in labor-management matters, instead preferring a hands-off policy.

The administration's view toward labor relations apparently had little to do with the decision to keep the group outside the ranks of governmentment, however.

The committee is basically the same group that served as an official advisory board on labor-management matters in both the Nixon and Ford administrations under Dunlop. The group continued briefly during the Carter administration but split apart when key management members refused to endorse labor law reform legislation being pushed by the unions.