NZEI president Lynda Stuart said centres were being forced to "drive down quality" because of a freeze in the per child funding rate that was continued in last month's Budget.
Early Childhood Council chief executive Peter Reynolds said many smaller centres were "questioning their viability" with frozen funding.
"Some of them can't increase their fees because they are operating in areas where the parents can't afford to pay more," he said.
NZ Kindergartens chief executive Clare Wells said kindergarten funding was cut by 14 per cent when the Government abolished a higher funding rate for services with 100 per cent qualified teachers in 2010.
Kindergartens have been funded for pay increases for their teachers, who are unique in the preschool sector in being part of the state sector and paid at rates agreed by the Government and NZEI. The latest increase of 2 per cent was agreed last week.
But Wells said that even with that increase, the per child per hour funding rate would still be below what it was before the 2010 cut.
"What has happened is that most kindergartens have an all-day licence," she said.
"That probably generates more funding. It also means that the ratios of teachers to children are higher."
Auckland Kindergarten Association is gradually moving its kindergartens to seven-hour days - a move its chief executive Tanya Harvey said was aimed at maximising the numbers of children who could get the maximum six-hour state subsidies, as well as meeting parents' needs.
She said kindergartens could still take children for half-days, but the "vast majority" of parents were opting for full days.
Alexander said the Education Act defined a free kindergarten as an early childhood service "whose licence permits no child to attend for a period of more than four hours on any day".
"Kindergartens will no longer be about children and meeting children's needs first and foremost," she said.
"Kindergarten association boards and managers must stop kindergarten as it is known in our society from being erased."
However, Harvey said sessional hours were not an essential feature of kindergartens.
"We are conscious of the philosophy of teaching as learning, learning through play, equal access," she said.
"If we had stayed with a sessional model there would be no kindergartens open, it's just not realistic with the demand from families.
"There is still a sessional option, but more and more we are finding that's not what families want."