The Educational Institute of Scotland (EIS) says a lighter workload would give teachers more time to work with pupils before the first round of the new National exams. The union wants the Scottish Qualifications Authority (SQA) to suspend its "verification" scheme, which assesses how teachers are grading pupils' work.
Allowing schools to opt in would help target schools in need while allowing others to use time to prepare for exams, the union said.
Larry Flanagan, EIS general secretary, said: "At this point in the school year, where exam preparation is vital, the most helpful thing that the SQA could do is act to lighten the pressure that is being placed on pupils and teachers by simplifying its verification procedures."
The call is supported by Alan McKenzie, acting general secretary of the Scottish Secondary Teachers' Association, who said: "This is a sensible proposal allowing a little flexibility for hard-pressed schools to ease the workload burden that is now accepted as a barrier to the successful implementation of the Nationals."
However, Dr Janet Brown, SQA chief executive, said external verification was a critical component of the quality assurance process.
She said: "The external verification process is designed to build confidence in the assessment system, and we have seen clear evidence in many subjects and in many centres of a sound understanding of the standards and good assessment practices.
"We have fed back to the schools that were sampled in the first round and will continue to supply information to all schools highlighting good practice and providing feedback.
"We will continue to discuss verification with teacher associations and others to ensure that the process supports the maintenance of national standards, while allowing teachers time to focus on coursework and exam preparation."
This is the latest controversy to hit the National exams, which were introduced as part of the new Curriculum for Excellence (CfE) reforms and will be sat by some 54,000 15 and 16-year-old pupils from April.
In January, a survey of teachers highlighted a raft of concerns with staff struggling to understand the purpose of the changes.