In a rare intervention, the former prime minister said a shift to the left after the party’s crushing general election defeat would be to treat voters as if they were “stupid”.
His comments, to the centre-left Progress think-tank, came as the first public opinion poll in the Labour leadership contest put left winger Jeremy Corbyn on course for a shock victory.
Mr Blair derided the veteran backbencher as the “Tory preference” and said the party could not regain power if it was simply a “platform for protest” against cuts.
“It would not take the country forwards, it would take it backwards,” he said. “This is why when people say ‘My heart says I should really be with that politics’ - get a transplant.”
Mr Corbyn hit back at Mr Blair’s “very silly remarks” and dismissed claims he would split the party.
He told the Press Association: “Can’t we discuss the policy issues that we are putting forward in this election about rebuilding our society, rebuilding our economy, eliminating poverty? Let’s stick to issues.”
With the unexpected surge in support for Mr Corbyn threatening to plunge Labour into a bitter civil war, Mr Blair warned it could not win on an “old- fashioned leftist platform”.
He compared the position facing Labour to the 1980s when the party swung to the left under Michael Foot, paving the way for nearly two decades of Conservative rule.
“The Labour Party persuaded itself that the reason why the country had voted for Margaret Thatcher was because they wanted a really left-wing Labour Party,” he said.
“This is what I call the theory that the electorate is stupid, that somehow they haven’t noticed that Margaret Thatcher was somewhat to the right of (defeated Labour prime minister) Jim Callaghan.”
Mr Blair’s intervention came as research by YouGov for The Times found Mr Corbyn was the first preference for 43% of party supporters - way ahead of bookies’ favourite Andy Burnham on 26%.
Shadow home secretary Yvette Cooper was on 20% and Liz Kendall 11%.
The study also forecast that if Ms Kendall and Ms Cooper were eliminated and second preferences redistributed under the alternative vote system, Mr Corbyn would beat Mr Burnham by 53% to 47% in the final round.
The suggestion that Mr Corbyn - originally seen as the rank outsider - could turn the the tables and win was greeted with anger and dismay among leading figures on the centre and right of the party.
Shadow education secretary Tristram Hunt warned that Labour could be reduced to a “pressure group” that would not have “broad reach into all parts of the United Kingdom”.
John McTernan, a former special adviser to Mr Blair in Downing Street, turned on Labour MPs who had “lent” their nominations to Mr Corbyn to “broaden the debate”, even though they did not want him as leader.
“They need their heads felt,” he told BBC’s Newsnight. “They are morons.”
In a keynote speech setting out his economic policy, Mr Corbyn said austerity was a “political choice not an economic necessity”.
He promised a “publicly led expansion and reconstruction of the economy” while protecting public services and increasing taxes on the wealthy.
Labour former frontbencher Emily Thornberry criticised Mr Blair for some of the “stupid” attacks he made.
“I thought that some of his off the cuff comments were unworthy of him,” she told BBC Radio 4’s PM.
Ms Thornberry defended her decision to nominate Mr Corbyn despite supporting Ms Cooper.
“I nominated Jeremy because I think he represents an important body of thought within the Labour Party,” she said.