American Telephone & Telegraph Co. will lower long distance rates an average 3.5 percent, effective today, the company said yesterday. ATT said the move will save consumers about $772 million a year.

At the same time, the Federal Communications Commission disclosed that it would look into whether AT&T could lower its rates further and told the company to submit additional financial data.

AT&T's cuts are largest for daytime use, with an average 6.4 percent reduction in that category. Evening rates were trimmed by 1.9 percent and late night and weekend calls by 0.6 percent. Cuts also were announced in WATS and other business services that AT&T offers.

Generally, business users will benefit more than residential users, AT&T said, Residential customers will save about 21 cents on an average monthly bill of $9, or 2.4 percent. Price cuts were focused on business services, company spokesman Herb Linnen said, because AT&T's competitors have been putting particular pressure on it in these areas.

Other long distance companies are expected to follow the lead set by AT&T, the country's dominant carrier.

"We will be reducing our prices but have yet to determine to what extent and when," said Kathleen Keegan, a spokeswoman for MCI Communications Corp., the country's No. 2 long distance carrier. "We will first review the AT&T filing and make a decision."

U.S. Sprint Communications Co., which ranks No. 3, said it intends to "remain competitive" with AT&T and will "file appropriate action with the FCC in the very near future."

The cut is AT&T's sixth since 1984 and pares the cost of its long distance services by 36 percent since then.

Like the previous five, this reduction is based on AT&T passing along to consumers savings it will realize by paying lower fees to local telephone companies for using their networks to begin and end long distance calls. As such, the lower rates consumers will pay starting today will not cost AT&T anything, as they will be matched dollar-for-dollar by savings in what it pays out for access fees.

Access charges are set by the FCC. Last week it ordered the local companies to cut those collected from AT&T by about $772 million. AT&T then got to work calculating new rates to reflect those savings.

The FCC yesterday held out the possibility of additional rate cuts if it is shown that AT&T's overall cost of doing business will decline in 1988. The commission said that when it filed for new rates, the company had failed to include overall financial data that is routinely filed with rate change applications. The commission instructed the company to provide it and AT&T agreed to do so.

Of particular interest to the commission, officials there said, is savings AT&T may enjoy next year due to changes in tax laws and pension programs and potential added costs due to investment in new transmission facilities. "We don't have the information at the moment to say whether the sum of those and other potential changes is positive or negative," said Gerald Brock, chief of the FCC's common carrier bureau. "But we feel that to fulfill our regulatory responsibilities we need to see that information."

Meanwhile, AT&T personnel yesterday were busy sending out the new rates, in many cases by facsimile machine, to the approximately 1,150 local phone companies around the country that act, for a fee, as billing agents for it.

Computation of long distance charges is based on several factors, including geographical distance, duration, discounts for minutes after the first minute, and time of day or week the call is made. Rate changes can thus require extensive reprogramming of phone company computers that automatically keep tabs.

AT&T has known the basics of the new rate structure since November and programmers at the companies have been at work punching the new data into their machines. Yesterday, the final numbers, base rates in cents per minute for varying distances, derived from the $772 savings in access charges, were sent out.

The programming work that remained so that a call made at 12:01 this morning would reflect the new rates was not very big, according to Doug Wilcox, AT&T's federal regulatory division manager.