American Telephone & Telegraph Co. yesterday proposed to cut long distance rates an average 3.6 percent, saving consumers $800 million a year -- but only if it can do so painlessly by cutting its payments to local phone companies by the same amount.

It is now up to the Federal Communications Commission to decide next month on how far the company will be allowed to drop long distance rates on Jan. 1. AT&T's competitors, whose rates are not subject to regulation, are widely expected to match whatever cuts the big company makes.

In a filing with the FCC yesterday, AT&T projected an average 3.6 percent rate reduction. The cut would be contingent on the FCC approving an $800 million drop in fees that AT&T pays to local phone companies for their help in routing long distance calls.

The companies, however, are saying that AT&T's payments to them should be cut by only $200 million. In that case, consumers would get savings of only that amount.

AT&T is optimistic that the FCC will decide in its favor. "We have gone into very thorough investigation and justification of that difference," said Larry Garfinkel, vice president for marketing. Many analysts expect the FCC to set the figure somewhere in between.

AT&T pays nearly $20 billion a year in access charges, accounting for about half its operating expenses. The fees are set on the basis of traffic and expenses projections, with the long distance and local companies haggling over what is fair each year at this time.

MCI Telecommunications Corp., the country's second-largest long distance company, declined comment yesterday on AT&T's proposal, saying it would wait to see what the FCC decides on the access charge question.

"MCI intends to maintain its competitive position relative to AT&T," said a spokesman. It and third-ranked US Sprint Communications Co. have generally priced their services below those of AT&T, which controls about 75 percent of the long distance market.

AT&T is proposing to apply bigger cuts to daytime service rates than to nighttime discount ones. Profit margins are generally higher on the full-rate day traffic, which the company says is split almost evenly between business and residential callers.

Daytime callers would get a 6.3 percent cut under AT&T's plan, evening callers 2.2 percent and late night and weekend callers 0.8 percent. Customers of toll-free 800 service would get a 2.9 percent reduction, while WATS customers would save 4.4 percent.

In a separate filing yesterday, AT&T proposed rate increases of $128 million a year for rates charged to users of private lines. This would reflect higher access charges for these services from the local phone companies, it said.