The Educational Institute of Scotland (EIS) said changes intended to reduce assessment under the new Curriculum for Excellence (CfE) had failed to have an impact.
The warning comes after a report from a left-of-centre Scottish think tank called for the current system of exams to be scrapped and replaced with a single exit qualification.
The Reid Foundation report said an over-reliance on tests - partly driven by the university sector - was undermining the education system.
Larry Flanagan, general secretary of the EIS, said: "The report raises key questions about the purpose of education and we are sympathetic to many of its conclusions. The EIS is clear there has been significant over-assessment in the first year of the CfE programme in secondary and exit-only exams would be an idea worth considering in any review of CfE implementation."
Parent groups also warned against a system overly driven by exams. Eileen Prior, executive director of the Scottish Parent Teacher Council, said: "The report... seems likely to chime with many people who want to see greater pace and momentum in the direction of travel already established in our education system."
Joanna Murphy, vice-chair of the National Parent Forum of Scotland, added: "We agree that too much emphasis on exams does not benefit all children and we would hope that, as CfE becomes more familiar to all, a better balance that results in young people's achievements, skills and successes being better recognised will be one of the benefits.
"However, society as a whole still places a big emphasis on exam results which puts schools, parents and young people under pressure to focus on this more than other areas."
A spokesman for the Reid Foundation said: "There is a risk that education policy in Scotland is trapped in a feedback loop.
"Children are put into an exam competition and parents are scared their children will lose the competition so they encourage them to compete. This is then taken as consent from parents for a competitive system.
"Actually, it would be better for both the development and the general happiness of pupils if we just let them learn and stopped testing them to death."
A Common Weal: Education was written by Brian Boyd, emeritus professor of education at Strathclyde University, in Glasgow. It states: "The present national assessment programme, with its heavy emphasis on timed, pencil-and-paper exams, is no longer fit for purpose."
Instead, the report calls for a single qualification in the last year of school.