Mr Blair has admitted Labour defied his predictions and secured a “remarkable result” at last month’s General Election under Mr Corbyn’s leadership, which has raised the party’s hopes of returning to power.
But the ex-premier issued a caution about the “risks of an unchanged Corbyn programme” for the UK.
In an essay for his own Institute for Global Change, Mr Blair – the last Labour leader to win a general election – claimed Britain would be “out for a long count” if Brexit was followed by Mr Corbyn entering Downing Street.
He wrote: “If a right-wing populist punch in the form of Brexit was followed by a left-wing populist punch in the form of unreconstructed hard-left economics, Britain would hit the canvas, flat on our back and be out for a long count.”
Responding to Mr Blair’s intervention, Mr Corbyn insisted one of his predecessors as Labour leader was “perfectly entitled to give any opinion he wishes, as is anybody else”.
But he added: “I hope they would recognise that politics has changed, the idea of trickle-down growth in wealth of people simply doesn’t work.
“There has to be a redistribution and that is what our manifesto was proposing.”
Mr Corbyn suggested Mr Blair would recognise the support both he and US Senator Bernie Sanders, a fellow anti-austerity campaigner, enjoy “indicates there’s a thirst to do things very differently” with a “more inclusive, more socially just, more egalitarian approach to the world rather than just subsidising the very rich”.
Asked whether the former prime minister’s comments were helpful to the debate over Britain’s future relationship with the EU, Mr Corbyn replied: “Anyone’s entitled to give their views and I listen to all of them.
“The views we have are that we want to see tariff-free access to the European market, protection of European nationals and protection of the labour rights and environmental conditions and consumer rights that we achieve through EU membership.
“I hope Tony Blair and everybody else recognises that is what our position is and that we do recognise the results of the referendum a year ago.”
The Labour leader spoke after addressing a rally in the Southampton Itchen constituency, as Mr Corbyn conducts his tour of Britain’s most marginal seats.
He claimed those who attended his speech on Saturday could see last month’s General Election was “a staging post to the next one where we will win a majority”.
Also responding to Mr Blair’s comments on a future Corbyn government, Labour shadow chancellor John McDonnell suggested the ex-premier “hasn’t really listened to the nature of the debate that is going on in the pubs, the clubs and school gates etc.”