Cambridge Assessment, the parent body of the OCR exam board, says key stage 2 test results, by which the children are to be selected for the extra attention, are unreliable guides to future progress.
It said it would be unfair to use them to single pupils out and pointed out that famous scientists such as Einstein and Newton were late developers and could have been disadvantaged by such an approach.
It added: "Children progress at different rates and to base such life chances on tests at an arbitrary point in time would be unwise."
The Specialist Schools and Academies Trust is working with the Government to encourage universities to establish links with pupils who have excelled in the key stage 2 tests in their early secondary years.
Universities will be asked to contact the children's families, suggest they join holiday courses or summer schools.
Secondary heads will be told the names of top-performing pupils and that they will be held accountable if such students do not get three A grades at A-level.
Sir Cyril Taylor, chairman of the trust, does not want bright 11-year-olds overlooked as a result of a poor secondary education and has argued that top-achievers at 11 should achieve three grade As.
But Cambridge Assessment, whose research division released a statement on the issue, says the figures do not bear this out. It said that more than half of the top 5 per cent of pupils at GCSE in 2004, were not among the top 5 per cent at key stage 2 five years earlier.
Although it did not have figures for A-level, the link with KS2 achievement was likely to be even weaker because of the greater time between the KS2 tests and A-levels.
The tests were also not meant to be aptitude tests to predict future performance. And the fact that they were only set in three subjects, whereas A-levels offered many more disciplines, raised further questions about their validity as predictors of A-level performance.
Sir Cyril was out of the country. The trust said it was supporting the Government in building a register of gifted and talented pupils at secondaries.
The Department and Education and Skills said that KS2 results would not be the only criteria by which pupils would be selected for extra attention.
But it was unable to say which other factors would be used, as it said these were still being decided upon.
A spokeswoman said: "This is not about selecting at 11 the pupils who are going to go on to university. It is about identifying the support that gifted and talented children might need."