Schools may face legal action if inspectors find they are failing to improve educational opportunities for ethnic-minority pupils.
The proposal is one of several put forward in a government report this week to boost the achievement of children from different ethnic groups, particularly African-Caribbean pupils. Their GCSE results declined last year while those of almost all other ethnic groups improved.
The report blames institutional racism and low teacher expectations caused by "racist stereotypes".
The strategy was published alongside the first set of official Department for Education and Skills figures for GCSE results by ethnic group. These will now be produced annually.
Schools minister Stephen Twigg told The TES: "We need to recognise that institutional racism does have an impact in education."
"But what is clear from the evidence in the report is that racism cannot be the only reason for these gaps because the greatest achievers are from ethnic minorities, notably Indian and Chinese communities."
Teachers and the public have until May 28 to respond to the draft, Aiming High. The DfES will unveil final plans in the autumn.
A key proposal is to make the Office for Standards in Education judge whether schools and local authorities are complying with the amended Race Relations Act.
The Act requires schools to promote equality of opportunity and good relations between different ethnic groups, as well as monitoring schemes to help each group.
Schools that are not doing enough will be issued with compliance notices by the Commission for Racial Equality. The CRE will launch legal action if they continue to fail to comply.
Other proposals include:
* Work to cut exclusions of ethnic groups;
* improvements to training in race issues for teachers; and
* national schemes to raise the achievement of African-Caribbean pupils and bilingual students.
Mr Twigg said the number of exclusions of black Caribbean boys could be cut by "questioning teachers' assumptions" about them, and by greater parental involvement, though he would not be setting a target for this. They are four times more likely to be excluded than their peers.
CRE chairman Trevor Phillips applauded the strategy. But Dr Tony Sewell, an expert on race issues and director of the Hackney Learning Trust, said it did not go far enough in addressing the needs of African-Caribbean pupils.
Dr Sewell said Indian and Chinese pupils achieved better results because their parents "shared the attitudes of the white middle class" and had a "migrant mentality".
* Lambeth this week reported that 13 of its schools have raised achievements of African-Caribbean pupils above national averages.
Interview with Trevor Phillips, Friday magazine, 10 "Aiming High: Raising the Achievement of Minority Ethnic pupils" is available from email@example.com