A House Republican group recommended yesterday that the Interstate Commerce Commission, the nation's oldest independent regulatory body, be abolished by the end of 1987 and its few remaining functions transferred to the Department of Transportation and the Federal Trade Commission.

The report by the Task Force on Congressional and Regulatory Reform of the House Republican Research Committee comes as the Reagan administration is deciding what to do with the remnants of various transportation regulators.

Various proposals, including one that closely approximates the recommendations of the task force, are receiving "active consideration," a White House official said.

The ICC, which once held tight rein over rates, fares and places served for all railroads, truckers and interstate bus companies, has found itself with less and less to do as deregulation legislation for those industries has taken hold.

Rep. Jerry Lewis (R-Calif.), chairman of the task force, said, "The public can best be served by sunsetting the ICC." The Civil Aeronautics Board, which once regulated all routes and rates for airlines, is already scheduled to go out of business in 1983, with its remaining regulatory duties going to the Transportation Department.

The task force recommended that the Federal Trade Commission be given jurisdiction over intercity moving companies and other consumer protection responsibilities currently handled by the ICC. Economic regulation of railroads plus insurance and safety functions for trucks and buses should go to DOT, the task force said. Anti-competitive pricing questions should be referred to the Justice Department, it said.

The task force rejected a proposal being pushed by Sen. Bob Packwood (R-Ore.), chairman of the Senate Commerce Committee, that the remnants of the ICC, the CAB and the Federal Maritime Commission all be placed in one "superagency" that would retain the character of an independent regulator.