Blair said as the details of what Brexit meant for the country began to emerge: "If the will of the people shifts, why shouldn't we recognise that?"
Blair, who was premier from 1997 to 2007, told the BBC the 48% who had voted to Remain in the EU felt "disenfranchised" and it was not clear "what we are moving to".
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When asked whether "keeping our options open" meant a second EU referendum, Blair replied: "It means whatever we decide it should mean as we see how this debate develops."
The 63-year-old Labour politician added that when the practical effects of the UK's decision to leave the EU became clearer, "then Parliament's got a role, the country should carry on being engaged in this debate, it should carry on expressing its view...
"We are sovereign. Let's just keep our options open," he added.
Ahead of the historic June 23 referendum, Blair had warned that "our nation is in peril" after the vote to leave the 28-nation EU and the negotiations on the UK's future relationship with the other countries would be of "extraordinary complexity".
In an article in the Daily Telegraph, Blair had said: "There is going to be a negotiation of extraordinary complexity where there are a thousand devils in every detail. Those we used to call 'our European partners' are, unsurprisingly, divided and uncertain themselves."
He said some countries wanted a quick divorce, while others favoured a delay in commencing the article 50 process, which starts a two-year countdown to Brexit.
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