Ministers want schools to work "more extensively and effectively" with parents, who they say are the most important factor in helping pupils to achieve. They also want schools to offer parents wider support and become better at identifying vulnerable children and families.
But teachers' leaders say that the central business of schools must remain academic achievement.
In a document entitled 21st Century Schools, published this week, the Government says some schools are not doing enough to identify vulnerable children who may be at risk of abuse.
"Many schools remain uncertain about their exact role in early intervention," the document says. "Some schools feel they are able to identify issues but do not always get the right support from other agencies to follow up concerns."
The document is being used to launch a consultation on the next stage of school reforms. A White Paper setting out how the Government expects to achieve this is to be published in the spring.
At this stage there is little detail, but ministers are clear that the changes they envisage will lead to a very different schools system, with much more emphasis on parents.
Jim Knight, Schools Minister, recently told heads: "If we're really serious about narrowing attainment gaps, we've got to put more of our focus on parents."
He gave the example of a Swindon primary where teaching assistants were teaching English to "adults in the community" as well as to pupils.
But Mary Bousted, general secretary of the Association of Teachers and Lecturers, said: "The state and society has to be realistic in what it can expect schools to do. The core business of schools always has to be academic learning."
She said more resources would be needed to help schools improve their links with parents and there had to be a clearer framework setting out who was responsible for what in safeguarding children.
The document agrees on this last point, but does stress schools' central role.
"Schools are the main universal service for children and young people and may be the only children's service with which some families are in regular contact," it says. "As such, schools play a key role in identifying any additional needs children and families might have and helping them to receive the support they need - either from the school itself or from other children's services in the local area."
The consultation runs until Tuesday, March 3. The document can be viewed at: http:publications.dcsf.gov.ukeOrderingDownloadDCSF-01044-2008.pdf.