European heavyweights Germany and France backed a "multi- speed" Europe after Britain's divorce with the union.
But Polish Prime Minister Beata Szydlo said she would never back such a plan, which is also opposed by some eastern European states that fear being left behind.
The 27 EU leaders -- without British Prime Minister Theresa May -- struggled to draft a declaration that is to be unveiled at a March 25 summit in Rome to mark the EU's 60th birthday.
Leaders have stressed the need to pull together as the European Union comes to terms with Britain's seismic decision to leave the bloc.
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The EU 27 will "work together to promote the common good on the understanding that some of us can move closer, further and faster in some areas, keeping the door open to those who want to join later," said a draft of the Rome proposals.
The wording clearly prioritises a "multi-speed" Europe and drew ire from countries like Poland who are loath to see EU heavyweights go it alone, but also fear for the large subsidies they get from Brussels.
Szydlo singled out outgoing French President Francois Hollande for criticism, accusing him of trying to "blackmail" Poland at the summit.
"Am I supposed to take seriously the blackmail of a president who has a four percent approval rating and who soon won't be president?" she said, without giving further details of what Hollande had done.
Tusk, a former Polish premier, backed the drive for unity but also cautioned: "If you want to go fast, go alone, if you want to go far, go together."
"This is seen as introducing a new dividing line, a new kind of iron curtain between the east and west. That is not the intention," Juncker said.
The struggle to forge a more unified future for Europe was overshadowed by the clash with Poland over Tusk's re-election as head of the European Council, which groups the bloc's political leaders.