Tony Blair has been accused of "insulting the intelligence" of voters and "arrogance" after he urged opponents of Brexit to "rise up" against leaving the EU.
The former prime minister said voters backed severing ties with Brussels without knowing the true cost and should have the chance to change their minds.
In a speech in London, Mr Blair questioned whether the referendum had given a mandate for "Brexit at any cost".
But his intervention has drawn the ire of Brexit supporters, with Foreign Secretary Boris Johnson accusing him of "insulting the intelligence" of those who voted to leave.
The leader of the official Vote Leave campaign in the referendum said: "I respectfully say to Tony Blair, those who call the British people to rise up against Brexit, I urge the British people to rise up and turn off the TV the next time Blair comes on with his condescending campaign."
Former Cabinet minister Iain Duncan Smith told Sky News Mr Blair "seems to have forgotten what democracy is about" and accused him of "arrogance".
And Michael Gove, another prominent Leave campaigner, said: "Politicians like Tony Blair should respect the result and work with the Government to make a success of Brexit instead of trying to undermine British democracy."
In an impassioned speech, Mr Blair rejected the idea that leaving was now "inevitable", adding: "I accept right now there is no widespread appetite to re-think.
"But the people voted without knowledge of the true terms of Brexit. As these terms become clear, it is their right to change their mind. Our mission is to persuade them to do so.
"I don't know if we can succeed. But I do know we will suffer a rancorous verdict from future generations if we do not try.
"This is not the time for retreat, indifference or despair; but the time to rise up in defence of what we believe - calmly, patiently, winning the argument by the force of argument; but without fear and with the conviction we act in the true interests of Britain."
Mr Blair acknowledged that concerns over immigration were a big reason for the Leave victory - but said Brexit would only give the UK control over 12% of migration to Britain.
The three-time election winner also warned that leaving the EU gave the SNP a more credible case for Scottish independence.
Mr Blair hit out at Jeremy Corbyn's Labour, saying that in the absence of what he called an effective opposition, pro-Europeans needed to build a movement that reaches across party lines.
"The debilitation of the Labour Party is the facilitator of Brexit. I hate to say that, but it is true," he told the audience.
In response, a Labour source said: "No wonder we are still trying to recover from Tony Blair's legacy when he has such contempt for democracy.
"What he doesn't seem to realise is people voted Leave precisely because they felt let down by 13 years of the Davos leftism he is still trying to flog."
Mr Blair's rallying cry has sparked speculation he would like to create a new pro-Remain political party made up of Blairites, Liberal Democrats and even some pro-EU Conservatives.
However, he denied this after a question from Sky's Senior Political Correspondent, Robert Nisbet.
Answering questions after his speech, Mr Blair also rejected suggestions he should shoulder some of the blame for Brexit because he failed to impose controls on immigration from the EU when he was in Downing Street.
Mr Blair, who was in office from 1997 to 2007, said the majority of migration occurred after 2008.