More than 30,000 people have backed a "kid's strike" boycott of the SATs exams next week.
The Let Our Kids Be Kids campaign wants parents to keep their children off school, saying they are "over-tested, over-worked and in a school system that places more importance of test results and league tables than children's happiness and joy of learning".
A petition on the 38 Degrees website backing the plan to keep children at home on May 3 had more than 32,000 signatures on Saturday morning, including people claiming to be teachers.
In an open letter to Education Secretary Nicky Morgan, published on their website, the Year Two parents behind Let Our Kids Be Kids said they "represent the voice of parents across the country" who "want an end to SATs now".
They wrote: "Please take a long, hard look at this. Do you want your legacy to be the confident cancellation of unneeded and unnecessary SATS, showing you are listening to your electorate and the teachers you claim to support ... or the overseeing of a shambolic testing regime desperately unwanted by millions of people to the point that this country saw its first open parent revolt?
"You have the power to stop these tests. NOW. Our children, our teachers and our schools deserve better than this."
SATs (Standard Assessment Tests) are taken by children aged six or seven in Year Two and then again in Year Six, aged 10 or 11, before a third set in Year Nine aged 13 or 14.
Parents are being urged by the campaign to keep their children off school for "a day of educational fun instead" and its website includes a model absence letter for parents to hand to schools.
The letter says: "It seems that we have reached a point where action needs to be taken; we are aware that some teaching unions will be balloting members with a view to boycott the upcoming 'SATS' and hope that you and your colleagues will be a part of this - an action that would receive huge backing from parents across the UK.
"However, we also feel that it is time that parents join teachers in taking a stand. These are our children and we must stand up for their rights."
#letourkidsbekids The youngest has decided to take action on Tuesday. l will not stand in his way
-- joanne phillips (@jo_pipsqueak) April 29, 2016
I'm climbing a mountain with my boy on 3 May. He is more than a statistic. #letourkidsbekids
-- Kate Taylor (@katectaylor) April 29, 2016
The Times reported that some headteachers who are backing the campaign plan to mark absences as "educational" rather than "unauthorised".
A Department for Education spokesman said: "Only exceptional circumstances warrant a child being taken out of school during term time.
"We are clear that tests should not be a cause of stress for pupils - they help us ensure schools are performing well, and we know the best schools manage them successfully."
He added: "We know mastering the basics of literacy and numeracy at primary school has a huge impact on how well children do at GCSE, which is why we are determined to raise standards."
Russell Hobby, general secretary of the National Association of Head Teachers, said school leaders were "immensely frustrated" by the situation.
"As leaders of schools they want children in school. As an association we are not condoning people taking them out of school but it will be the choice for the individual head as to whether to authorise this or not," he said.
"They can manage through this - the tests that are sat next week for the younger children are only one item that goes into feeding assessing their performance and actually the results that are eventually reported to Government are the teacher judgments not the test results so I don't think it affects the running of the school.
"But to get to this place where you've got teacher, head teachers and now parents saying the testing regime has gone awry, I think it needs a rethink."