In his boldest comments on testing since becoming head of the Qualifications and Curriculum Authority in 2002, Ken Boston said: "A good amount of the testing currently done at seven, 11 and 14 could be marked by teachers."
Under a new system which Dr Boston said could be introduced over 10 years, pupils would no longer sit externally-marked tests in May.
Instead, teachers would select tests to give to their pupils when they chose throughout the year, from a "bank" of assessments similar to the current tests. They would mark the tests themselves, with a sample of perhaps 30 per cent sent away to be moderated by external examiners.
Speaking at a conference to launch the QCA's first annual report, Dr Boston said that there was need for caution over any changes. Some external assessment could be retained, initially, for the key stage 3 tests.
But scrapping the bulk of external key stage assessment would have several advantages, including reducing the need to find thousands of markers every year.
Schools could also hold the tests at a time convenient to teachers, so they fitted in with pupils' programmes of learning. They could get the results sooner than at present, and then use them to respond to pupils' learning needs.
The new testing system would still be compatible with league tables, he said. All schools' seven, 11, and 14-year-olds would continue to be tested.
Their results would be aggregated to give results for each school as well as statistics for the whole of England.
"This might all be 10 years away, but I think it's perfectly feasible," he said.
However, Dr Boston's call is unlikely to be taken up by the Government.
Ministers are placing more emphasis on teacher assessment at KS1 from this year. But they have resisted all calls to do so at KS2 and 3.
A Department for Education and Skills spokesman said: "Tests and targets are here to stay. National tests at 11 and 14 boost standards and help achieve the best for every child.
"They help provide independent, objective benchmarks of performance, and parents have a right to this information."
Dr Boston also reignited the debate on the future of A-levels, suggesting the exams could eventually be absorbed into a new diploma structure planned for vocational courses.
He said: "If all of us who believe in this reform are successful, the question in 10 years' time will not be, 'Why would you bring the A-levels and the diploma together?', the question will be, 'Why would you not?'."