Education Secretary Nicky Morgan has signalled she wants to see more robust tests for seven-year-olds, insisting they must provide a "firm basis" for measuring pupils' academic progress.
In what was billed as her first major policy speech since the election, Mrs Morgan indicated a rethink of Key Stage One evaluations that could see them standardised nationally again.
She also confirmed that a new National Teaching Service (NTS) is being created, recruiting 1,500 of the "brightest and best" teachers by 2020 to work in the toughest schools.
The individuals will stay with schools for up to two years, and receive fast-track promotion opportunities as an incentive to take part in the scheme.
The plans for more testing were condemned by teaching unions, with Kevin Courtney, deputy general secretary of the National Union of Teachers, warning they would be "educationally harmful, unreliable, costly and damaging to children".
"The UK already has the most excessively tested children in the whole of Europe," he said.
Dr Mary Bousted, general secretary of the Association of Teachers and Lecturers (ATL), said changes to testing would not improve standards of maths or English.
"We support the Government's commitments to help schools enable more children to achieve expected standards of English and maths at primary school," she said.
"But continual testing is not the answer and nor is changing the goalposts every time a minister speaks."
Mrs Morgan told the event hosted by the Policy Exchange think-tank that the coalition government "raised standards and heightened expectations".
But she highlighted local authorities such as Knowsley, Salford and Rochdale in the North West where the majority of pupils were still not securing five good GCSEs.
She stressed the importance of "reception baseline" assessments in reception class and "more rigorous" SATs at the end of primary school.
"If children haven't mastered the basics in primary school, the rest of their time in school is a game of catch-up. Maths and English are the non-negotiables for a successful life, and children who don't master them at primary school are much - much - less likely to succeed when they move to secondary school," she said.
"To be really confident that students are progressing well through primary school, we will be looking at the assessment of pupils at age seven to make sure it is as robust and rigorous as it needs to be.
"We'll be working with head teachers in the coming months on how we get this right, holding schools to account and giving them full credit for the progress they achieve."
Mrs Morgan also announced a new target for secondary school pupils to study the core subjects of English, maths, science, history or geography and a language at GCSE - the subjects included in the English Baccalaureate performance measure.
Currently around 39% of pupils study these subjects but the Education Secretary will today announce a consultation on the Government's goal for that to rise to 90%.
A survey by the Association of School and College Leaders released in August suggested many headteachers were against such a move because of concern that the reforms will not suit every pupil and could mean less time for more creative subjects.