Responses to a government consultation on changes to primary assessment in England revealed disappointment at the plans, which the DfE hoped would improve educational outcomes and reduce teachers' workloads.
Currently all children undergo a development check at the end of reception year - the early years foundation stage profile - when they are five.
They also complete national tests, known as Sats, in English and maths in Key Stage 1 (KS1) at age seven, and Key Stage 2 (KS2) at age 11.
The DfE has suggested lowering the reception-class baseline for testing to a younger age, making KS1 tests non-statutory, and correlating reception testing outcomes with those for KS2.
In its response to the consultation, teachers union NASUWT argued the reforms would "result in little more than the replacement of one high-stakes form of assessment with another".
"Amending the statutory assessment system on this basis would serve only to risk significant increases in teacher and head teacher workload with no educational benefits for pupils," it said.
NASUWT general secretary Chris Keates said: "It is clear there is much more that needs to be done in terms of making sure the national assessment system is fit for purpose and inspires the trust and confidence of the public and the teaching profession.
"If ministers are serious about reforming assessment in a way which frees teachers up to teach then they must also review the high stakes nature of the accountability system to ensure it helps, rather than hampers, teachers to raise standards of educational achievement."
Association of Teachers and Lecturers (ATL) general secretary Mary Bousted welcomed plans to remove KS1 Sats, but was opposed to plans for "an experimental reception baseline assessment".
"At a time when our schools are struggling to make ends meet, and teachers are being shouldered with unacceptable levels of workload, more tests cannot be the answer," she said.
In its response, ATL argued that early education should not be about shaping children for school.
This opinion was backed by charity Early Education, which strongly opposed the introduction of the new baseline.
However, the National Foundation for Educational Research (NFER) backed the DfE's plans, and called for a "standardised assessment" for reception-year pupils.
"Once a reception baseline for measuring progress is established, assessments at the end of KS1 should be made non-statutory," the organisation's submission said.
"Annual monitoring of standards should occur at the end of KS1 via nationally representative sampling and using externally marked KS1 tests."
The DfE's consultation ran from 30 March until 22 June 2017.