The Chesapeake & Potomac Telephone Co. of Virginia, backing off its previous stand in hopes of appeasing skeptical legislators, today promised to maintain low, flat-rate economy service at the same time it is promoting its controversial "local long distance" service.

Local long distance, or measured local service, would charge residential customers according to when, where, and how long a local call lasts.

The service, which a senior telephone official of C&P's parent Bell Atlantic Co. once said "may be our number one objective," has been sharply criticized in Maryland and the District, as well as in Virginia.

"In D.C., with overwhelming community opposition, it has been turned down three times," said Mark L. Plotkin, a Washington activist and leader in the fight against measured service. "A call from Arlington to Washington would be a long distance call.

All of this is a larger game to make local service a luxury rather than providing universal, affordable service," Plotkin said.

"This is a victory for consumers," said state Sen. Clive L. DuVal (D-Fairfax) of C&P's decision today.

"They were ultimately going to squeeze everything else except local long distance rates out."

DuVal, vice chairman of the legislature's joint study committee on telecommunications, which met here today, said he still may introduce legislation requiring the company to keep its economy service as an option.

Under a flat-rate system, low-income customers pay a small fee to hook up to a telephone and are charged a specific amount for each use. Another low-cost option allows a certain number of calls for one fee and then charges a specific amount for each additional call.

Under so-called measured local service, approved as an option last year, customers would be billed much as they are for long distance now. Critics say it would hurt consumers because it would be difficult for people to keep track of each call and budget for what are now mostly fixed monthly costs.

C&P plans to introduce measured local service to residential customers in Arlington and Alexandria in 1986, the first communities in Northern Virginia to receive the service, which would initially be optional. Company officials had indicated that if they received Virginia State Corporation Commission approval they would eventually phase out other economy plans in favor of measured service.

DuVal, a longtime advocate of lower telephone and other utility rates, said that C&P and the nation's other telephone companies have not proven that billing customers for local calls in the same way long distance calls are measured is either necessary or fair. "All that C&P knows is that it will get more money," DuVal said.

A similar measured service is available as an option in Maryland. A bill to bar measured service died in a Maryland legislative committee last year after strong opposition from C&P officials in that state.

The Virginia State Corporation Commission, which regulates utilities, approved the measured rate service as an option beginning in 1984. So far, of C&P's 1.3 million residential customers, the service is available to about 100,000 customers in Southwestern Virginia, the Hopewell area and some Eastern Shore communities.

"We've have had no complaints from customers," said Sid Philips, a C&P Virginia lobbyist who made the pledge today to maintain the economy flat-rate service. "We are not going to remove the untimed" options.