Praising the deal reached earlier this week to reduce Greece's debt burden as an unprecedented commitment by eurozone governments to keep the crisis-wracked state within the single currency, Coeuré told an economic forum in Paris there needed to be closer political coordination to manage crises.
"The notion that the euro is a currency without a state is in my view misguided," he said.
"The euro is a currency with a state - but it's a state whose branches of government are not yet clearly defined."
Commenting on possible steps in the right direction, Coeure said he supported the idea of a single eurozone Treasury and eventually common euro bonds.
He insisted that for its part, the ECB would do everything within its mandate "to ensure price stability in the euro area and therefore trust in the euro as a currency," he said.
Greece's international lenders on Monday agreed on a package of measures to reduce Greek debt by €40 billion, cutting it to 124% of gross domestic product by 2020.
Although the technical details have yet to be finalised, Coeure said, he pointed out this was the first time finance ministers had jointly committed to keeping Greece in the euro.
Commenting on the ECB's own measures to prevent the eurozone falling apart, Coeuré highlighted the central bank's new bond-purchase programme, dubbed Outright Monetary Transactions (OMT).
OMTs aim "to price out a type of catastrophic risk premium that investors demand in conditions of market paralysis," Coeuré said in the text of a speech for delivery at the forum.
"It was breakdown risk in the early stage of the crisis, the risk that the payments system would seize up completely. It is break-up risk now," he added.