A focused visit to the local authority found that children's social workers had manageable caseloads ranging from 22 to 24 children, and they felt positive about working for the authority.
However, the report said Manchester needed to go further to receive a "good" judgement above its current "requires improvement" rating achieved a year ago.
Provision had been rated as "inadequate" in September 2014, with inspectors warning that several hundred children had waited "a considerable" time for a social work assessment, citing high caseloads as part of the cause.
But inspectors said there have been significant improvements since then.
"Staff say they feel listened to and supported, and they demonstrate passion and commitment to improving the lives of vulnerable children," the inspection report states.
"Senior managers have been successful in creating an environment which is conducive to continued improvement."
The report noted many other areas where practice had improved, in particular, in children's statutory reviews.
These, it said, were being held regularly, were attended by relevant professionals, children were encouraged to participate and attend, and review minutes were found to be detailed and include children's views.
The report described independent reviewing officers' reports as "excellent".
"Reports are written directly to children," it said.
"The language used and the sensitivity with which circumstances and decisions are explained evidences excellent child-centred practice."
Practice was also found to be effective within multi-agency working, family group conferences and inspectors thought the department was basing decisions for children to become looked after on thorough and well-written child and family assessments.
However, the report stated the authority needed to do more to improve assessments after children had come into care. It criticised the authority for not following up routinely, and not providing clear insight into events and changes children had experienced.
It described care plans as "weak", with insufficient detail about the child's needs, interventions, aspirations, overall plans for permanence and contingency arrangements.
"Planning for some children is based on out-of-date information and the child's plan is not reflective of their current situation," said the report.
Inspectors also noted social workers were not undertaking life-story work with all looked-after children, and only a few had used impact chronologies as a method of informing assessments and planning.
However, the report acknowledged that Manchester had implemented training and coaching to improve social workers' use of impact chronologies as a result.
Paul Marshall, director of children's services at Manchester City Council, said: "As Ofsted have noted in their letter, we have a good understanding of our strengths as well as the things we still need to improve.
"We've put measures in place, including an ongoing programme of training and development for staff, to ensure these further improvements are made.
"While it's too soon to see the impact of this, we're confident this will come and that the service will continue to improve."