Proposals set out in the Green Paper suggest that, by 2004, 85 per cent of pupils leaving primary school should reach the required standard - level four - in both subjects.
It also suggests a new target of more than a third of pupils achieving the next level.
Ministers expect to reach the original target of 80 per cent of pupils achieving level four in English and 75 per cent in maths by 2002. But schools are now being consulted on a futher push on standards that will require a ten percentage-point improvement in maths and five-point rise in English over two years.
Ministers also want 35 per cent of pupils to reach level 5 in English and maths by 2004. Currently 29 per cent achieve this level in English and 24 per cent in maths.
According to David Hart, general secretary of the National Association of Head Teachers, such targets would put pressure on schools.
"Heads are not against challenging targets, but these cannot be imposed unless more account is taken of school intakes and the way league tables are onstructed," he said.
"As it stands, pupils that are absent for the test are recorded as having scored zero and that can have a significant impact on a school's results."
John Bangs, head of education at the National Union of Teachers, said heads were complaining that the proposed targets were unrealistic.
"Schools have not been consulted. Scores have become very high stakes and even those schools with a stable set of children and no staffing crisis will have problems improving year-on-year.
He said schools were already under pressure because the Office for Standards in Education used a fall in results as one of the indicators to judge if a schools needed to be re-inspected."
Alongside the focus on improving the basics, primary schools are to be required to offer "a rounded and enriched education" and to provide extra-curricular sports, arts and citizenship programmes.
However, guidance from the Qualifications and Curriculum Authority on they ways that schools can fit all these requirements into the day will not be available until June. The guidance was due in schools last September, but has had to be revised.