After considerable internal debate and external pressure, the advertising industry told Congress yesterday that it supported Federal Trade Commission Chairman James C. Miller's proposal to limit the agency's power to regulate deceptive advertising.

Reversing an earlier position, the nation's three leading advertising trade groups told a House subcommittee that they now have been "persuaded by the arguments" put forward by Miller and other business groups that "the deceptive standard was overly broad" and needs to be limited.

Initially, the American Advertising Federation, American Association of Advertising Agencies and the Association of National Advertisers had said there was no need to change the FTC's authority on deceptive advertising. Yesterday, however, they called for legislation that would not permit the FTC to challenge deceptive advertising unless the commercials "consist of material representations known to be false or made in reckless disregard of their truth or falsity" or unless the misrepresentations result in "substantial economic injury" to reasonable consumers.

Additionally, the three groups that comprise more than half of the persons and companies in the nation's advertising industry asked Congress to eliminate the FTC's authority to attack advertising it considers unfair, as it once regarded television ads aimed at children.

According to industry and agency sources, the advertising groups agreed to change their earlier testimony after considerable pressure from the National Association of Manufacturers, the U.S. Chamber of Commerce and Miller himself.

The advertising proposals are similar to those recommended by Miller, who is the first FTC chairman in the agency's 68-year history to propose cutbacks in the agency's powers.

Under the advertisers' restrictions, several FTC officials say the agency no longer would be able to require advertisers to substantiate all the claims in their ads. They also say it would be more difficult for the agency to attack misleading ads such as false performance claims.

"We are not seeking to destroy or weaken the FTC in any way," testified William W. Rogal, general counsel for the American Advertising Federation. "Insofar as advertising is concerned, we believe that a national regulatory body is needed."