They argue the decision to wait until a child turns five when they could take up a place aged four costs the authority more money.
In the past they have said the delay could contribute to pupils leaving school without gaining any formal qualifications.
The argument, focusing on the financial implications, has met fierce criticism from councillors and education experts who say there is not enough evidence to back up the claim.
Councillor Alison Johnstone, education spokeswoman for the Greens, said: “If the council hopes to save money by reducing what it sees as avoidable deferrals, it must provide robust, comprehensive evidence to show that this is in the best interests of our pupils.”
Education bosses want to reduce the number of parents choosing to wait until their children turn five before sending them to school and are targeting parents to try to get them to chance their minds.
Edinburgh has a high level of deferrals, with the figures three times higher than in council areas of a similar size.
In a report to the council’s education committee this week, education director Gillian Tee said: “Delaying school entry has resource implications. If the council approves an additional year, there is a cost.
“At the same time, valuable early resources tied up in this way restricts the development of other provision in early years.”
She added that sending children to school at an earlier age “reduces the risk of young people reaching statutory school leaving age before fully completing their school education”.
But opposition councillors and non-elected representatives on the education committee, including educational experts, questioned the claims and called for further evidence on educational performance and cost-saving to be provided.
Cllr Johnstone added: “The evidence is narrowly focused, reports only on research from North America and doesn’t provide any information from those Scandinavian countries whose later school starting age appears only to benefit educational attainment.”
City education leader, Cllr Marilyne MacLaren said: “Our decision to give parents the arguments in favour of not deferring entry to P1, as a matter of course, is firmly based on a robust study of 36 international and Scottish research papers about the disadvantages of delaying school entry.
“P1 teaching and personalised learning means that a young child’s needs can be met and talents can be developed at the pace which suits them.
“The additional resources freed up by not delaying entry, can be better used to give every child an improved start in life.”