England's chief exams regulator has suggested the national curriculum tests pupils sit at 11 and 14 might be marked by teachers, not external examiners.
Any change would depend on strict conditions being met
Ken Boston of the Qualifications and Curriculum Authority said they might not have to take place simultaneously.
He was speaking at the launch of the Institute of Educational Assessors, which aims for better assessment.
The Department for Education and Skills said there was "absolutely no question" of ending externally marked tests.
Currently, pupils across England sit the same question papers at the same time on the same day for each subject, and their answers are marked by external assessors working for an exam board.
Dr Boston said assessment was "the key feedback loop to guide and shape further learning".
Teachers did it all the time - but until now there had been no way of recognising nationally, or setting a benchmark nationally, for the occupational standards and skills required to be a high quality professional assessor.
"Assessment is also a vexed and contested area, professionally and politically," he said.
He would reject the idea that teacher assessment might mean teachers would set their own tests and decide on that basis what level a child had attained, because it would be impossible to "strike a common standard".
But there were circumstances in which it might be something the QCA could recommend to the government for primary schools and in the early secondary years, he said:
The whole issue of testing provokes strong feelings in England's schools because of the use of the results in government tables of school performance.
- if teachers had access to a national bank of standard-referenced tests and examinations
- these had been piloted by test developers and exam boards under QCA regulation
- they were administered within a specific window of time
- papers were marked using a mark scheme on which teachers had been trained
- their marks were externally and independently audited by chartered assessors belonging to the Institute of Educational Assessors
- the system was demonstrably as rigorous and robust as the current system in maintaining standards nationally and producing valid and reliable data on national performance
Children at the end of their primary schooling are sitting tests this week. Those aged 14 took theirs last week.
The leader of the National Association of Head Teachers, Mick Brookes, suggested recently that schools could disrupt next year's tests by asking parents to send their children in late.
He said his members were "sick to the back teeth" of the pressure tests created.
Dr Boston said it was important that the new institute "maintains its independence and becomes the captive of no lobby".
Governments had a responsibility to provide valid and reliable national data on educational performance and school performance, as well as ensuring each child's attainment was reported to parents, he said.
A spokesman for the Department for Education and Skills said external tests would stay.
"They provide the most reliable, objective and consistent measure of what young people have achieved and offer clear and widely-understood measures of progress for every child.
"They are also vital for public accountability."
Professor Roger Murphy of Nottingham University, writing in the first issue of the new institute's journal, said one of the "myths" about exams was that they were the most reliable barometer for judging educational standards.
Groups of pupils and schools changed from year to year.
"Judging government, local education authority or even school performance simply on the basis of changes in GCSE or A-level grades obtained in different years is a hazardous process," he said.