Formal contract negotiations between representatives of the striking telephone workers' unions and officials of American Telephone & Telegraph Co. resumed here for the first time in 10 days yesterday, while striking union members and supporters gathered to hear Washington area labor leaders promise to stay with them on the picket lines as long as the strike lasts.

The bargaining sessions resumed amid reports that the three unions--frustrated by their inability to bring phone service to a halt--may have found another bargaining tool in their effort to win concessions from AT&T and its subsidiaries. In several parts of the country, including the Washington area, local union representatives have asked state regulators to reconsider pending local rate increases or to figure the impact of the strike on those proposals. It was unclear yesterday what action, if any, would be taken by regulators here.

Yesterday, Pic Wagner, a Washington spokesman for AT&T, called the Communications Workers of America initiative "silly and spurious."

Last weekend, after a request by the New York chapter of the CWA that the state link rate cases to company savings on wages during strike action, New York Attorney General Robert Abrams said the New York Telephone Co. is saving $30 million a week on labor costs and that he recommends that the state's Public Service Commission suspend rate tariffs and investigate the possibility of reducing local phone rates as long as the strike lasts.

A similar request was forwarded last Friday to Mayor Marion Barry and to the governors and attorney generals and to the public service commissioners of Maryland, Virginia, West Virginia and Pennsylvania. CWA officials said yesterday that if the New York and Washington area initiatives are successful, the union will file similar petitions in every state.

In separate mailgrams addressed to Barry and each of the governors and attorney generals, the regional vice president of the CWA, George Strick, argued that, "given current conditions it is appropriate for the D.C. government and each of the four states to demand that business and residential customers receive a rebate . . . for the obviously inferior service offered . . . and the lower overhead enjoyed by the company."

Strick said yesterday that C&P Telephone Co. is saving $13,672,500 a week on salaries in the Washington area while the strike lasts. "Consumers shouldn't subsidize the company's profits while the strike is on," he said. CWA officials are said to believe that their proposal has a high chance of success in New York and in the District.

Wagner said, however, that rate-making was not a retroactive process. "The proper procedure is at the end of the year to see if the company achieved the rate of return authorized by the state's commissioner," Wagner said. "If it hasn't, you increase the rates. If it has, you put in some rate reductions."

Yesterday, AT&T vice presidents met with the vice presidents of the three striking unions, CWA, the International Brotherhood of Electrical Workers and the Telecommunications International Union, to discuss what reportedly were a new set of proposals made by the company.

Company officials said that negotiations with the International Brotherhood of Electrical Workers, which represents 100,000 striking workers, and with the Telecommunications International Union, with 50,000 striking members, had continued throughout the day.

Representatives from the CWA met for two hours yesterday morning with company officials and reportedly recessed later in the afternoon to evaluate a series of new proposals made by AT&T. Negotiations resumed last evening, then recessed until this morning. There was no word on precisely what was discussed. Negotiations between AT&T and the CWA, with its 525,000 striking members, are considered a bellwether for the bargaining sessions' progress.

When negotiations broke down Aug. 6, CWA's contract demands included a 7 percent pay increase and a cost-of-living adjustment, but job security and employe retraining have emerged as the key issues in the strike.

At the small noon rally yesterday, speakers repeatedly addressed the issue of automation and how it effects job security, and discussed the public perception that after 10 days, the strike has not had a dramatic effect on the nation's phone service.

Local labor leaders said the telephone strike was a harbinger for a new technological era in which workers can no longer paralyze an industry by walking off the job.

"Organized labor knows only too well that what takes place here will be a forerunner for the rest of the unions," Josh Williams, local head of the Central Labor Council, told the crowd. Earlier, he said the rally was called in solidarity with the phone workers because "if they do not succeed we know it will be open season on all unions."