CINCINNATI (AP) _ Federated Department Stores and Allied Stores Corp., operating under protection of the federal bankruptcy laws, have reached an agreement to resolve more than $588 million in claims.

The retailers said Thursday that they had reached agreement with JMB Realty Corp., which together with some of its affiliates had filed more than 500 claims against Federated and Allied.

Those claims alleged that the retailers failed to live up to terms of a 1983 real estate development agreement between Federated and its subsidiary, Federated Stores Realty, Inc., and JMB and two affiliates, Center Partners Ltd. and JMB-Federated Realty Associates.

Federated and Allied, which sought court protection under Chapter 11 of the bankruptcy laws while reorganizing $7.7 billion in debt, must receive approval of the agreement from U.S. Bankruptcy Judge J. Vincent Aug Jr.

Allied's chains include Jordan Marsh, Maas Brothers, Stern's and The Bon Marche. Federated's chains include Abraham and Straus, Bloomingdale's, Burdines, Lazarus and Rich's-Goldsmith's.

The proposal would allow Center Partners to obtain $28 million in general unsecured claims in the retailers' reorganization plan. Federated would give JMB 134 acres of undeveloped land in Memphis, Tenn., and would transfer its interests in several projects to JMB, under terms of the 1983 agreement.

Federated and Allied also would assume contracts and unexpired leases for store operations in 17 shopping centers owned by JMB, primarily in Florida and Georgia.

In Florida, those stores include Burdines at Coral Square Mall and Broward Mall in Fort Lauderdale, Volusia Mall in Daytona Beach and Miami International Mall; Burdines and Bloomingdale's stores in Town Center at Boca Raton; and Maas Brothers-Jordan Marsh at Governors Square in Tallahassee.

In Georgia, the stores include Rich's at Marketsquare in North DeKalb, Gwinnett Place near Atlanta, Shannon Mall and Cobb Town Center in Atlanta, and Augusta Mall in Augusta.

Also, Lazarus at Dayton Mall, Dayton, Ohio; Bloomingdale's in Riverside Square, Hackensack, N.J.; Abraham and Straus at Galleria in White Plains, N.Y., and Monmouth Mall in New Jersey; Goldsmith's at Hickory Ridge Mall, Memphis; and The Bon Marche in Eastridge Mall, Casper, Wyo.

James Zimmerman, president of Federated and Allied, called the proposal ''a fair and equitable resolution of a number of issues which ... moves us one step closer to the Federated and Allied's ultimate emergence from Chapter 11.''