An Interstate Commerce Commission proposal that moving companies give consumers binding estimates for shipping their household goods won the general support of the Justice Department yesterday.

In comments filed with the ICC, the Justice Department said such a plan could give the consumer a greater range of price and service options, encourage price competition in the highly regulated industry, and reduce the "inordinate number of inaccurate estimates" now facing consumers.

But Justice said it is worried that other aspects of the existing regulatory structure could discourage the movers from offering binding estimates despite consumer demand for them, depriving the shipping public both of potential benefits of the proposed system and also of the current estimating services, albeit inadequate, which the proposed ICC rules would eliminate.

Justice's comments were made in response to a May proposal by the commission to overhaul the way the household goods carriers do business. The estimating practices of the industry have been under attack almost constantly, and the commission has revised its procedures several times in an attempt to protect the consumer better.

Currently, the carriers offer nonbinding estimates to shippers on request. If the actual charge exceeds the estimated charge by more than 10 percent, payment of the excess is deferred for 15 business days. The system has spawned the common underestimate and also the practice of weight bumping, increasing the final weight of a shipment in order to overcharge the shipper.

The proposed rules would replace entirely the current regulations. They would allow carriers, at their option, to give binding estimates based on the constructive weight of the shipments. The estimate would be the final charge unless the charge based on actual weight is less; in that case, it would apply.

There is a possibility movers may not offer binding estimates should the rules be changed. Movers could decide collectively not to or decide the process might add costs they don't want to incur.

To guard against that, Justice suggested the ICC amend its proposal to require that carriers give either the binding or the non-binding estimates. However, it repeated its long-held preference for deregulation of the household goods moving industry.

"Competition will resolve the problem of inaccurate estimates as well as others plaguing the industry and represents the only means of ensuring improved industry performance and increased consumer protection," Donald L. Flexner, deputy assistant attorney general in the Antitrust Division, said yesterday.