Last week, 300 Year 1 children in primary schools took the test, as part of the pilot scheme.
The petition, launched by TACTYC, the association for the professional development of early years educators, has now been signed by more than 1,300 people.
The group has joined forces with a campaign started by the president of the UK Literacy Association, David Reedy.
Its supporters include teaching unions and members of the Cambridge Review team.
Mr Reedy told Nursery World, 'What we're trying to do is to get the Government to think again about the phonics test for six-year-olds. We're bringing together all the associations that have worries about this. The Government said in their White Paper that it wasn't their place to tell teachers how to teach, but this test does just that.'
He added, 'We think phonics is essential, but it is not the be-all and end-all to teaching reading. The new Ofsted framework has an explicit focus on reading by the age of six and inspectors are told they will need to use the outcomes of the test in their judgements on how reading is taught.'
Janet Moyles, early years consultant and former chair of TACTYC, said, 'While phonics is vital in children's learning to read, it should not dominate the literacy curriculum. Most conscientious teachers assess children's phonics knowledge and use this as the basis to ensure children learn appropriate skills.
'If a phonics test is introduced, it will inevitably lead to "teaching to the test" and limit children's literacy learning to certain skills rather than an overall love of books and understanding that meaning and knowledge can be obtained through reading.'
An evaluation of the reading test pilot is being carried out by Sheffield Hallam University and will be published in the autumn.
Alison Peacock, head of Wroxham Primary School and network leader of the Cambridge Review
'Teaching phonics is only one strategy of many. Just to focus on synthetic phonics is a very limited approach to reading. As soon as you start to test every child, you have to ask: what is the test for? Schools already assess children in the EYFS by observing children's progress. I'm against the notion of a test because my fear is that it's about holding schools to account, not about checking children's progress. There is a risk that there will be unintended consequences - it could distort the curriculum and diminish the chance of children learning to read.'