American Telephone & Telegraph Co. yesterday asked the government for permission to more than double the rates it charges its long-distance competitors to hook into the Bell System's local telephone network.

In a tariff request filed with the Federal Communications Commission, AT&T said that, beginning May 2, it planned to boost the current monthly fee its long-distance competitors pay for each Bell System connection from $122.20 to $258.21.

The request, which was immediately denounced by AT&T's long-distance competitors, must be approved by the FCC. However, several FCC officials have indicated that it is very unlikely the commission will permit AT&T to raise these rates as high as it wants. Instead, these officials have indicated that the commission most likely will accept a 50 percent hike in fees to $180 a month pending a more detailed study of AT&T's request.

AT&T has argued that higher rates are needed because the current rates are so far below costs that AT&T ratepayers are subsidizing the long-distance competitors by six cents for each minute the hook-up is used.

"The tariff filing means quite simply that the charges these companies pay should be based on the true costs and should be borne by them and not by our customers," said AT&T spokesman Pic Wagner.

AT&T's competitors, however, have argued that they already are paying AT&T far too much for the service they receive. "There is no way they could possibly justify these rates," said William G. McGowan, chairman of MCI Communications Corp. of Washington, the leading non-Bell long-distance company. According to McGowan, MCI should be paying no more than $50 a month for each of its connections because that is the fee most other telecommunications companies pay to hook into AT&T's local network.

Additionally, McGowan and other long-distance firms question the basis on which AT&T seeks to raise its rates, calling its justification inadequate and inaccurate.

AT&T's request for a rate hike was made possible by an FCC decision earlier this week in which the agency rejected AT&T's request to boost its hook-up rate to $330 a month. Instead, the commission agreed to keep intact for two more years the specific formula which AT&T and its competitors had negotiated for hook-up fees.

However, at the same time, the commission gave AT&T permission to adjust several of the factors that make up the formula to reflect inflation and the competing phone companies' increased use of these connections.

AT&T took advantage of that decision yesterday, arguing that inflation had driven up the cost of the rate per minute from 5.95 cents to 6.58 cents. Additionally, AT&T said that, given the increased business of these long-distance companies, use of the connections has increased from 3,000 minutes a month to 5,823.