In a move interpreted by some as a job application, the former prime minister said the EU could do with a strong leader approved by the people.
He also warned that too deep a political divide between Britain and the core eurozone countries could lead towards a break-up.
"Out of this European crisis can come the opportunity finally to achieve a model of European integration that is sustainable," said Mr Blair. "A Europe-wide election for the presidency... is the most direct way to involve the public."
Europe's millions of residents might feel "alienated" unless they have a direct say in who is governing them, Mr Blair told the Nicolas Berggruen Institute on Governance.
"An election for a big post held by one person - this people can understand," he said. "The problem with the European Parliament is that though clearly democratically elected, my experience is people don't feel close to their MEPs."