The Evangelical Alliance Scotland wants to discuss the proposal, outlined in the Scottish Government's Children and Young People Bill, and reach "consensus" with Children's Minister Aileen Campbell.
Director Fred Drummond said: "While we do not doubt the government's sincere intentions behind this bill, these proposals raise serious concerns about the role of the state in modern Scotland, have massive implications for the role of parents and appear to be begging for a fight in the law courts as some parents may wish to challenge it, because it is not immediately apparent whether it is lawful under the European Convention on Human Rights (ECHR)."
The proposal to appoint specific named persons from the NHS and councils to monitor every young person's well-being from birth to 18 is considered one of the most controversial aspects of the Bill.
Ms Campbell insists it will help "provide a safety net for those who need one".
The Church of Scotland has already claimed that the change risks diminishing the role of parents "with no obvious benefit for the most vulnerable in society".
It has been criticised by the six former moderators of the Free Church of Scotland and the current moderator.
A Scottish Government spokeswoman said: "We are confident that the Bill is compliant with the ECHR.
"Families are not required to accept advice or offers of help from the named person. Any actions or advice from the named person must be fair, proportionate and respect rights with the aim of safeguarding the well-being of the child."
The bill is due to be debated by Holyrood at its final stage on Wednesday.
Ms Campbell has said "misunderstandings about the named person provisions are misinforming views".