Stephen Anwyll, former head of the national literacy strategy and now a senior official at the Qualifications and Curriculum Authority, said other forms of assessment needed to be promoted and reinforced.
Mr Anwyll is leading a QCA trial aimed at strengthening in-class assessment of pupils by teacher. He said that the trial had been welcome by all those who tried it.
It is due to be made available to all primary schools from January.
Speaking at an Association for the Study of Primary Education conference in Bath, Mr Anwyll said there were three types of assessment: the checks on pupils' knowledge that teachers carried out every day in class; the periodic judgments and reports they wrote on children's progress; and public tests. The latter tended to dominate, he said.
"Many people would say that what the public bit of assessment does is to have a negative effect on what happens in the classroom," he said.
"It has a narrowing effect: teachers teach to the test because it is a public form of assessment, and the periodic aspect gets bypassed."
Many teachers, he said, did not view national testing as useful to them but saw it as designed only to provide information for the next teacher on the level pupils had reached.
The conference heard Mr Anwyll report on the new system of teacher assessment - Assessing Pupil Progress - which has been trialledat key stage 2 in more than 100 primaries over the past two years. It is an approach already being offered to all secondaries at KS3.
The project involves teachers keeping files on each pupil and regularly assessing their progress against various criteria. This enables level judgments to be made on each aspect of a child's progress in reading, writing and maths, which can then be reported back to parents.
Mr Anwyll said that, initially, some teachers had found the process time-consuming, but after the first term they found it much less so. It also helped them to teach a much broader curriculum because all elements were assessed.
"Lots of teachers said: 'This has made me feel I'm now in control of assessment, that assessment belongs to me.'
"It really was quite striking that before (the trial) they felt that assessment was external to them: it did not belong to them," he said.
The trial materials are to be made available to all primary schools through the Primary National Strategy website in January.
Mr Anwyll said the materials are also likely to be used by the 10 local authorities that are piloting a new form of national testing from next month.
In the Making Good Progress pilot, pupils take key stage tests when their teacher believes they are ready for them. The materials could be central in helping teachers reach that judgment.
Robert Staples, head of Fairlands Primary in Stevenage, Hertfordshire, welcomed the trial as "fantastic", but said some local authorities had been pursuing the QCA approach for the past five years.