Councillor Mrs Marilyne MacLaren, convener for Education and Children and Families, said that both nursery head teachers and social care workers had reported an increase in behavioural problems in three- and four-year-olds.
Two years ago the Scottish Executive recommended that health visitors call on babies aged over six weeks on a case-by-case basis. Parents can still request health visitor support at any point.
'The people working in children's services I've met were not happy with this change of policy,' said Ms MacLaren.
'At a meeting I attended with nursery heads, two or three said they had children who clearly should have been on the health visitor radar but weren't.
'Children are slipping through the net and I'm campaigning to get a re-think on it,' she added. 'I think we need to have regular assessments with children under five in a consistent way.'
Her remarks come after a critical HMIE report on Edinburgh's child protection service published last week.
Ms MacLaren said, 'There are recommendations in the HMIE report and the inspection took place this year under new administration. It's a new regime, and we're determined to turn around the child protection committee.
'Already 40 babies have been taken into care since the beginning of the year because their parents are drug addicts,' Ms MacLaren added. 'We want to look at early intervention and prevention.'
A Scottish Executive spokesman said, 'There is nothing in the guidance to say that health visitors should stop visiting after six weeks, although in practice, contact after six weeks with the child and parents may be within a primary care setting.'