All children in England will be expected to know up to their 12 times table when they leave primary school, the government has announced.
Education Secretary Nicky Morgan said pupils aged 11 should also know correct punctuation, spelling and grammar.
"Getting English and maths right has to be at the core of our education system," she told the BBC.
Labour said the "surest way" to raise standards was to improve the quality of teaching in the classroom.
Under the Conservatives' plans, pupils would not be made to re-sit the new tests until they passed, but the school could be subject to measures if they failed.
A school that failed to get every pupil to pass the tests for two years running could be paired with an outstanding school to gain extra support. It could also become part of a teacher swap where heads of departments from good schools take over temporarily.
"We have to be ambitious for our young people. If you don't get it right at primary, then it becomes much harder for children to catch up at secondary school," she told BBC 1's Andrew Marr show.
In a wide-ranging interview, Mrs Morgan was asked about money and appeared to suggest the schools budget for pupils aged five to 16 would be ring-fenced.
"We're going to have more to say on schools funding very shortly but what I can say is that I am absolutely fighting for the schools budget to be protected," she said.
Key Stage Two tests already include questions on times tables and long division but pupils are given an overall mark, not for individual sections.
Mrs Morgan plans to make times tables a separate section within the maths test.
Nicky Morgan wants England's place in international education league tables to soar
In an article for the Sunday Times, Mrs Morgan wrote that she would "launch a war on illiteracy and innumeracy."
"We will expect every pupil by the age of 11 to know their times tables off by heart, to perform long division and complex multiplication and to be able to read a novel," she said.
"They should be able to write a short story with accurate punctuation, spelling and grammar.
"Some will say this is an old-fashioned view, but I say that giving every child the chance to master the basics and succeed in life is a fundamental duty of any government."
Mrs Morgan has set a new target for England to be the best in Europe, and among the top five countries in the world, for English and maths by 2020.
The latest Pisa league table, which ranks the test results of 15-year-olds from 65 countries, puts the UK at 26th for maths and 23rd for reading.
Shadow education secretary Tristram Hunt MP said Labour would reverse the rule change under David Cameron's government which allowed unqualified teachers into the classroom on a permanent basis.
"This is how we improve the learning and life chances for all children and raise our international position in reading, writing and maths," he said.
Liberal Democrat schools minister David Laws said no-one would take the Conservatives seriously until they committed to "protecting the education budget from cradle to college".
Christine Blower, general secretary of the National Union of Teachers, said "our children are among the most tested in the world" and "we do not need more of the same".
"Our schools need to be accountable, but the current system stifles creativity, leads to 'teaching to the test' and does not promote sustainable improvements in education," she said.
Russell Hobby, general secretary of the National Association of Headteachers (NAHT) described the new tests as a "gimmick" during the election season.
"Apparently head teachers will be sacked should any - yes, any - child fail the new test. We are all for aiming high but, remember, this is a short test taken by a young child," he said.
"Mistakes happen, children feel under the weather or have a bad evening beforehand. This does not mean that teachers are not working as hard as possible."
On the Andrew Marr show, Mrs Morgan was asked about the Independent on Sunday's lead story that former education secretary Michael Gove was still receiving paperwork from her department.
She dismissed the report as "complete nonsense" and said Mr Gove, who is now Commons chief whip, had been "nothing but supportive" since she took the job.
"The chief whip is of course going to see paperwork that goes for a number of departments... I know the chief whip has to be across all portfolio areas. But I am very much in charge of the education department," she said.