Nicola Sturgeon made the pledge as she opened the Teenage Cancer Trust's ninth international conference in Edinburgh.
16-18 Year Olds Should Be Exempt From New Law
Education Secretary John Swinney is being urged to rethink "absurd'' plans for youngsters aged 16 to 18 to be given a named person.
Ministers are currently seeking to clarify the controversial scheme in the wake of a Supreme Court ruling that the legislation, as it was passed by Holyrood, is ''incompatible'' with European human-rights laws.
Labour education spokesman Iain Gray said the legal setback gave the Scottish Government a chance to ``get the legislation right and restore public confidence'' as he insisted appointing a named person for youngsters aged between 16 and 18 was the "wrong decision''.
He added that making the change would be an "important step towards convincing Scotland'' about the plans after opponents of named person took the case to the Supreme Court.
Judges there decided information-sharing provisions in the scheme could result in disproportionate interference with Article 8 rights under the European Convention on Human Rights (ECHR) - the right to a family and private life.
Mr Gray has now written to the Education Secretary saying that as the Supreme Court had "effectively forced'' a pause in the legislation - which was due to be rolled out across Scotland at the end of this month - he should "take this chance to address wider problems'' in it.
In his letter, the Labour MSP said the Government had the chance to "show that you understand public concerns, and are listening to them, by going further than the court judgement requires''.
Mr Gray told the Deputy First Minister: "As you will have to amend the legislation, you should use the opportunity to remove 16 to 18-year-olds from the scheme.
"The extension of the law to young people already considered adult enough to leave school, work, vote and marry seems disproportionate and, to many, absurd.''
A Labour amendment, calling for the named person scheme to only apply to those up to the age of 16, was "voted down by the then SNP majority'' when MSPs approved the Children and Young People (Scotland) Act 2014, Mr Gray added.
"That was the wrong decision and has helped those who have tried to present the policy in as negative a light as possible to undermine confidence in its proportionality.
"Failure to listen and engage is the reason the scheme has lost public trust and now seems far removed from its original intentions - ensuring vulnerable children don't fall through the cracks and delivering the support that families need and deserve.
"Amending the Act now in this way would be an important step towards convincing Scotland that you are willing to listen to those who support the principle of this policy, but have lost faith in its implementation. This suggestion is made sincerely towards fixing this policy.''
The SNP introduced the flagship named person scheme to appoint a single point of contact, such as a teacher or health visitor, to look out for the welfare of children under 18.
Mr Gray argued that while the principle of providing support to vulnerable children was "sound'', the ``implementation of it has been a complete mess''.
He stated: "The SNP were not willing to listen to Labour's concerns at the time. That arrogance in government has come back to bite them.''
"Simply tweaking the Act to meet the Supreme Court's concern will not be enough.
"There has to be a complete revision of guidance and training materials, and adequate resources put in place for the professionals who will deliver the policy.''
A Scottish Government spokeswoman said: ``Clearly we are considering our detailed response to the court ruling.
"However, the named person service is intended to provide a central point of contact for parents and children from birth up to 18, which is in line with United Nations legislation which classifies children as young people under the age of 18.
"While some families may not wish to use the service, the legislation passed by Parliament would provide a legal guarantee of access to a 'named person' to ensure the child and their parents/carers can receive appropriate support if and when they need it.''
The 25 year old from Scotland was found dead on Saturday.
Major cities across Britain are becoming home to "hipster hotspots'' - pushing up house prices strongly in places such as Bristol, Manchester and Edinburgh as well as in London - research has found.
The Convention of Scottish Local Authorities (Cosla) has said that any more cuts to local government funding will result in "severe consequences'' for jobs across the country.
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