* EU's Juncker asks tough questions of euro zone leaders
* Debt crisis shows bloc's weakness as single currency area
By Francesco Guarascio and Robin Emmott
BRUSSELS, Feb 12 (Reuters) - The euro zone needs fundamental changes to the way it is run or faces endemic unemployment and the trap of low economic growth for years to come, the European Union's chief executive told the bloc's leaders on Thursday.
In a presentation, European Commission President Jean-Claude Juncker called for a deepening of the cooperation that underpins the 19-member currency area, despite the reluctance of countries to cede more sovereignty to EU institutions.
"There is a need to move gradually towards concrete mechanisms for stronger economic policy coordination, convergence and solidarity," said the presentation note handed out to EU leaders by Juncker and seen by Reuters.
Juncker warned that a failure to act would trap the euro zone in a scenario of low growth, depressed consumer prices and a limited ability to create jobs because "the legacy of accumulated imbalances remains painfully visible".
He challenged leaders to answer uncomfortable questions such as whether the euro zone eventually needs a finance ministry, a once unthinkable idea that the 2009-2012 debt crisis pushed leaders to consider.
But the euro zone's German-led integration process first launched at the height of its crisis has lost momentum since the European Central Bank stepped in decisively to stop the break-up of the bloc in July 2012.
The debate on integration has been complicated by some EU states pushing their national agendas. Germany sees the process as a way to toughen budget rules. Britain sees an opportunity to renegotiate its own position in the EU through treaty change needed for euro zone reform.
The bloc has taken many steps, including toughening its budget surveillance, setting up an emergency lending fund and a banking union with an agency to shut failing euro zone banks.
But Juncker, in coordination with ECB President Mario Draghi, European Council President Donald Tusk and Eurogroup President Jeroen Dijsselbloem, wants to go further. EU officials aim to present a report on that at an EU summit in June.
In his eight-page presentation, Juncker asked 12 questions, including: "What instruments are needed in situations in which national policies continue to go harmfully astray?"
That appeared to be a question partly directed at France, a long-running concern for the European Commission. The Commission has told Paris to cut public spending and reform its economy. (Editing by Louise Ireland)