The debate resumed after Question Time.
The UUP's John McAllister said it was incumbent upon members to make sure financial arrangements were put in place for kinship carers.
He looked forward to the time when Miss McIlveen brought forward her private member's bill on kinship care.
Pat Ramsey of the SDLP also referred to the financial need of those carers with "one extra mouth to feed, one extra child to clothe and care for".
Sinn Fein's Mickey Brady said one of the problems was that there was no legal definition of kinship care.
Replying to the motion, health minister Edwin Poots said his own mother had been part of a large family raised by their 14 year-old sister after their mother died.
He outlined the current legislation, whose guiding principle was that the child should grow up with its own family "when it is in their best interest to do so".
The minister said he welcomed the growth of kinship care in recent years but recognised that there were significant costs to the carers.
"A decision to place the child in any care arrangement must be in the child's best interests," he stated.
The minister also referred to his forthcoming adoption and children bill.
The motion was carried on an oral vote.
You can see the first part of the debate