Addressing the plenary in Strasbourg, Juncker said, "I repeat again that this is not about a two speed Europe. To say so is a misreading of the White Paper. Indeed, if German Chancellor Angela Merkel had not mentioned a two speed Europe no one else would have done so."
He added, "Nor is this about creating a new iron curtain between the east and west in Europe but, rather, it is about deeper EU integration and enhanced cooperation.
"I would like to see everyone in Europe involved in the debate on the future of the EU. The Commission does not want to dictate to anyone.
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"This narrow view of the EU just being about an internal market alone is not my choice. We need a wider debate."
The debate with MEPs comes 10 days before the 60th anniversary of signing the Rome treaty. It will be marked by several events next week in Rome.
Addressing Parliament, Italian Prime Minister Paolo Gentiloni agreed with Juncker, saying, "We cannot have a first and second class Europe, a Europe of the east and west. Everyone must be involved in this common European project. But at the same time Europe cannot stand still."
European Council President Donald Tusk said he hoped the Rome summit will be a "turning point" for the EU.
Malta's deputy Prime Minister, Louis Grech, representing the Maltese EU Council presidency, said, "Brexit is unfortunate we but cannot allow it to distract us. Talk of an existential crisis for the EU has become the norm and it would be a big mistake to underestimate the challenges. But it would be an even bigger mistake to do nothing and become negative. This would pave the way for the eventual erosion of the EU."
EPP group leader Manfred Weber said effort was needed to make Brussels and Strasbourg more acceptable to the public, adding, "We should not be seen as an external force that forces people into something they do not like. But this is something we should be saying every day."
S&D group Chair Gianna Pittella said, "urgent action is needed to relaunch the EU project."
He added, "But in Rome, we cannot speak in a vacuum or in slogans. Populism and Trumpism is currently very strong partly because we, the EU, have not been able to explain our achievements. But if we stand united we can face them down.
"The EU dream which existed 60 years has run into peaks of enthusiasm and then stagnation but we must save the EU project."
ALDE group leader Guy Verhofstadt said, "When talking about the EU's future it is often asked, do we need more or less? But that is a stupid question. We do not need EU regulation on cucumbers and bananas but, rather, a European border force, a European army and a European government for our single currency. We need less Europe in some fields and more in others.
"I hope the Rome summit does not produce hot air. The time now is to start a process on our future, finally, and not just make declarations. This process should be launched in Rome. I hope it can be the city of the rebirth of the EU."
Further comment came from GUE/NGL group Chair Gabriele, Zimmer who said she doubts "if Rome will signal a new start", while Greens co leader Philippe Lamberts hoped Tusk, in Rome, will prove "the man of the moment."
Ukip leader Paul Nuttall said he believes there will be a two speed, "with the UK in fast lane and all you guys going in reverse."
He said, "The Rome treaty was a grand plan, a noble idea, but it was of its time and, boy has this all now gone very much awry.
"The project has morphed into a political monster, which is egged on by eurocrats wanting more power. Brexit will trigger a floodgate where by others will leave the grand project you celebrate next week."
German S&D group member Jo Leinen said the problem was that "no one explains the EU benefits and why we need the EU.
"It has become less relevant so Rome can be an opportunity to remind people of the value of the EU. I hope the Council, at the Rome summit, will set the pulse for what we need to do."