Burnley Council has called for regular exams in 2021 to be scrapped as forcing pupils to take them as normal will have a “significant and deleterious effect”.
A motion passed by the authority calls on government to put in place “an alternative system of fair assessment”.
Councillor Margaret Lishman said the impact of Covid-19 meant holding traditional exams would see the “most disadvantaged” pupils “suffer most”.
The Department for Education (DfE) said exams will go ahead as normal.
The Liberal Democrat-proposed motion, shared by the Local Democracy Reporting Service, said the requirement for children to sit GCSEs and A levels in 2021 “will have a significant and deleterious effect on Burnley’s children in view of the education they have missed due to the Covid-19 pandemic”.
It added that holding traditional exams “may lead to discrimination in their choices of higher education”.
Ms Lishman, who proposed the motion, said some children had “completely disengaged from the school system” during the pandemic and those “who will suffer most are those who are already the most disadvantaged”.
She added that if the prime minister “truly wants to level up for the benefit of our children in the North West, he must find an alternative to top-down exams”.
No party currently controls the council, but its Labour leader Mark Townsend said the authority fully supported the campaign.
However, the council’s Conservative group abstained from voting on the motion.
The group’s leader Alan Hosker said exams were a “matter for the government, not the council” and added that he believed his Liberal Democrat colleagues were “indulging in political point scoring”.
A DfE spokesman said the government recognised pupils had “faced disruption”, but exams were “the fairest way of judging a student’s performance, which is why they will go ahead in England next year”.