In a move that will lower long-distance rates again, the Federal Communications Commission yesterday ordered local phone companies to reduce what they charge long-distance companies to connect with local networks.

The FCC ordered a $1.1 billion cut nationwide in these access charges, effective July 1. Long-distance carriers typically pass along to their customers savings from such cuts.

American Telephone & Telegraph Co., the nation's largest long-distance company, announced last month it would cut its rates by $160 million annually, effective July 1, in anticipation of the FCC decision. This would mean a cut of 2.5 percent in typical evening rates. Other phone companies such as MCI Communications Corp. and US Sprint Communications Co. usually follow suit to remain competitive.

AT&T has decided on deeper rate reductions, however, since it had based its cuts on local phone company proposals to the FCC. The local companies in April had asked to reduce their access charges by just $405 million on July 1.

But the FCC ordered an additional $696 million cut yesterday, saying the local phone companies had underestimated likely calling demand by about 2.4 percent, or 7 billion minutes.

The FCC also based its rate reductions, in part, on corrections of the local phone companies' cost estimates.

''There will be some further reduction beyond the $160 million AT&T proposed May 17,'' AT&T spokesman Herb Linnen said. He said AT&T probably would announce additional cuts next week.

''We expect AT&T to file reductions ... '' said Kelly Cameron, an official in the FCC's common carrier division. Cameron said the long-distance price cuts would not necessarily be a direct flow-through of access charge savings.

Before July 1989, when AT&T's earnings were restricted to about a 12 percent rate of return on its investment, the flow-through of costs generally were nearly automatic. But AT&T now is under a regulatory scheme that controls its prices within a prescribed range tied to the rate of inflation, not its profits.