The Federal Communications Commission granted American Telephone and Telegraph Co. a reduced interim rate increase yesterday for long-distance interstate and overseas services that is expected to generate $580 million in additional revenues annually.

Approval of the new interim rate of return, the first for the Bell System in four years, will permit the company to increase charges for interstate and overseas services by about 5 percent, FCC officials said.

The commission granted the new rate by a 4-3 vote, after rejecting At&t's request for a rate increase twice the size. AT&T had asked in March for approval for a two-step increase in the long-distance charges that would have increased revenues by 5.64 percent on June 1 and by a total of 10.5 percent as of Oct. 1.

Yesterday's action by the FCC authorized a 10.5 percent rate of return for At&t on its capital costs, one percent higher than the currently authorized rate of return. AT&T then is permitted to increase customer charges to reach the higher ceiling on its return.

The rate is an interim one, however, approved to permit AT&T's request for a higher, permanent rate of return of 13 percent.

AT&T may not be able to increase customer charges to the full amount authorized yesterday without exceeding the Carter administration's voluntary wage-price guidelines, an FCC official said.