680 of those have been recorded in the Kildare/West Wicklow and Dublin region.
An 'assessment of need' allows children to be diagnosed with a disability, such as autism, and then apply for the care they need.
The HSE is supposed to have these assessments finished within six months.
But according to new figures, which relate to the end of December, that target isn't being met in many cases.
A total of 3,256 assessments were at least three months overdue at that point.
They include 812 children in the north Dublin region, along with 650 cases in Cork and Kerry.
The HSE acknowledges the numbers of assessments overdue for completion remain high.
But it says there has been some improvement over the past two years.