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Jeremy Corbyn said 40,000 primary age children were taught in classes of 36 or more in England in 2016, blaming "broken promises" by the government.
But the Tories said the Labour leader's comments were "a massive own goal".
They said the Labour-led Welsh government had overseen increases in class sizes in Wales.
Meanwhile, Lib Dem leader Tim Farron is to target Conservative MPs who backed staying in the EU, challenging them to support his bid to stay in the single market.
With under seven weeks to go until polling day, parties are racing to select candidates and prepare for the snap 8 June election, announced by Prime Minister Theresa May on Monday.
Mr Corbyn, who insisted on Thursday that he can defy the polls and "change the direction" of the election, has used Labour analysis of Department for Education figures to focus on education.
He said: "The prime minister herself has said that super-sized classes are proof of a school system in a crisis.
"And that's what we've got on the Tories' watch.
"School leaders and teachers have said that Tory cuts to school budgets will mean class sizes will be forced to grow even larger. We cannot risk our children's education in this way."
A Conservative spokeswoman dismissed Mr Corbyn's comments and pointed out that the number of infants in large classes had risen by 18% in three years in Wales.
"Of course we are not complacent about the situation in England," she added.
"There is more to do and that's why we are spending a record amount on schools - something we can afford to do because of our careful management of the nation's finances."
Elsewhere on the campaign trail on Friday, Mr Farron will challenge Tory MPs who supported staying in the EU to oppose a so-called hard Brexit.
He will add: "If these Tory MPs reject these principles and back a hard Brexit manifesto, then people will know that on the biggest issue of the day they went missing in action."
Chalk and cheese. Black and white. Night and day. Ying and yang.
Theresa May and Jeremy Corbyn are not, repeat not, cut from the same cloth. Their fundamental beliefs differ enormously. Their solutions for society's problems are poles apart.
Politicians in opposing parties are sometimes friends across the boundaries. But it is hard, extremely hard, to imagine the Labour leader and the Tory leader ever quietly enjoying a pootle round the Berkshire countryside of a weekend, or a cappuccino in Islington in a quiet moment.
But right at the start of this election - whisper it - there is something significant they share.
Read Laura's blog in full