Juncker said that the case of Greece was "beyond comparison" with Ireland and Portugal, the two other eurozone countries to have benefited from an EU/IMF bailout.
Speaking only hours after chairing a eurozone meeting which approved a three-year, 78-billion-euro emergency loan programme for Portugal, Juncker admitted that a large part of the ministerial meeting had been in fact dedicated to discussing the situation in Greece.
Juncker was speaking at the inauguration of a new Brussels think-tank, the Government of the Future Centre, led by former Bulgarian Commissioner Meglena Kuneva. The think-tank is supported by Accenture, a global management consulting company, the College of Europe and the Lisbon Council, an economic think-tank and policy network.
The Eurogroup chief said that he disagreed with those who put Greece "in the same basket" as Ireland and Portugal. He argued that the main problem of Greece was a regression in terms of competitiveness.
In contrast, Ireland was faced with a real-estate bubble coupled with a banking crisis, whereas Portugal had protracted growth stagnation, he explained.
Juncker said that since it joined the euro zone, Greece's competitiveness gap had widened by 20%, while at the same time Germany had increased its competitiveness by 20%.
"Greece does not entirely respect the economic adjustment programme which we had agreed upon when we have put at the disposal of the Greek authorities guaranties to the amount of €110 billion. Therefore Greece needs to adopt, in the next few days, additional corrective measures concerning the budget deficit which continues to aggravate, instead of diminishing," he said.
Juncker added that Greece should adopt measures "of very large scope" to address the problem of its weak growth potential, and that the country should conduct privatisation "in a measure exceeding imagination, even Hellenic imagination".
Greece should rapidly privatise assets from its public sphere to the amount of €50 billion, as well as its national heritage, in a way that would bring its debt to sustainable levels in the medium and long term, Juncker went on.
"This debt is strictly unsustainable at the present time," he stressed.
Should Greece adopt all these measures, he said Athens would benefit from "soft restructuring," meaning rescheduling deadlines for debt reimbursement.
However, Juncker's idea appears to run counter a recent statement by German Chancellor Angela Merkel, who ruled out any restructuring of all three crisis-hit countries before 2013.
'Two things of which I am proud'
In more general terms, Juncker said that the enlargement and the euro were the EU's most important projects, without which the continent and the Union would have been much more vulnerable.
"We did two things of which I'm proud," he insisted. Thanks to EU enlargement East European countries, many of which were "predestined to oppose each other," had been locked in to safety, Juncker said.
Regarding the euro, he cited figures according to which the common currency had brought down inflation to low levels never attained by the Deutsche Mark. Without the euro, the Nordic currencies would be under-evaluated and vice versa, auguring "pernicious" developments, he argued.
Juncker also spoke out in favour of stronger economic governance and introducing "a minimum of European social rights". Europe is not a government, but the Union's rules make up for the absence of an EU government, he said. Regarding the absence of a social dimension to EU policies, which he lamented, he said he was not calling for equal salaries, but for "a minimum level of rules" in the social area.
Without naming any specific country, Juncker lamented the recent border row between France and Italy and Denmark's plan to reinstate "visible" border controls.
"I'm really upset to see that now, without any debate, and without taking into consideration the points of view of others, countries are reinstating border controls," he said.
Juncker regretted that "national concerns" had become predominant lately in EU affairs.
"If you have the choice between the national and the European avenue, even when in doubt, you should choose the European avenue, because national avenues lead nowhere," he said.
In search of new projects
Juncker also harked back to times when the EU had "projects and stronger institutions". In what can be seen as an allusion to the fact that the European Commission is often seen as accommodating the interests of bigger member states, he said: "Europe needs institutions which respect themselves and that stay respectable".
Juncker argued that Europe needed to define new such projects, citing hunger as one such possibility.
"As long as 25 children die every day from the most brutal death, that is hunger, it means that Europe is not a success […] We should have as a big European project to eliminate from the surface of the planet hunger and poverty. This should be a European project. Europe should speak to others, because the others are watching Europe," he said.
The eurozone chief also expressed sadness over the arrest of IMF chief Dominique Strauss-Kahn. He appeared to condemn statements by German and Belgian ministers, who have already called for the next IMF chief to come from an EU country.
"The question [of who should be the next IMF chief] is indecent. Let justice do its job," he said unequivocally.