The state Department of Children and Families and lawyers for a group of formerly neglected children are moving toward an agreement that could eventually end more than 20 years of court oversight of DCF.

The latest quarterly report by the case monitor said DCF had a "strong overall performance'' during April 1 through June 30.

Joette Katz, the former state Supreme Court justice, took over the sprawling, $800-million-a-year agency in January 2011. The reports by Wallingford-based court monitor Raymond Mancuso since the first quarter of last year have shown progress.

In the latest report, released Thursday afternoon, Mancuso said he reviewed the cases of 54 troubled children in state care throughout Connecticut. Of those, all of the child's needs were being met in 61.1 percent of the cases, a slight improvement over the 60.4 percent mark from the previous quarter.

Ira Lustbader, lead lawyer in the landmark child-neglect case that spawned the court oversight, said the percentage of cases in which children's needs are being met remains too low, but he acknowledged the improvement.

The number of children languishing in large residential centers continued to drop, and the number of children being placed in foster homes with relatives continued to increase, Mancuso reported. He said the department still needs more foster homes.

Mancuso reviewed the cases of 60 children who had been removed from residential centers and said there was no evidence they were being "rushed out"" of those centers due to department directives.

Katz has made it a priority to reduce the number of children living in institutions.

"There is considerable evidence of collaborative case planning'' before children are discharged from the centers and moved into foster families or other community settings, Mancuso reported.

Several problem areas remain, Mancuso said. While Katz and her cabinet are creating strong policies, sometimes the word isn't getting out to the field, Mancuso reported.

He said there is a need for more "proactive and consistent" case management and communication with families over services that are provided and outcomes for the children.

He said there remains "a variance in the proficiency and skill set" among social-work supervisors in the various regional offices, and an "inconsistency" with the way "supervision occurs as a practice statewide.''

Mancuso said that Katz and lawyers in the "Juan F." child-neglect case "reached an important agreement" that streamlines the way DCF can respond to concerns, and curtails the review process if the department demonstrates it can sustain improvement.

The Juan F. class-action lawsuit was filed in the late 1980s. The case led to a consent decree that will remain in force until DCF eliminates the problems that had it careening from crisis to crisis over much of the last 20 years.

Lustbader said the agreement Mancuso mentions in the latest report is "a great development. It's going to recognize the department's strengths and speed the eventual exit from the consent decree. There's going to be a lot less for the court monitor to have to do on the back end.''

Lustbader said Katz "champions the department's successes and owns the things that aren't going right. She dives in to address them. It's like night and day" from the previous administrations.