European Council President Donald Tusk has warned just days before an EU summit that the 28-nation bloc could break up under strain from mass migration and a deal to keep Britain in the union.

Speaking in Bucharest, Tusk warned Monday "this is a critical moment. It is high time we started listening to each other's arguments more than to our own."

He said it was "natural that positions harden closer to crunch time," three days before a "crucial" EU summit, which will have "the two biggest challenges to the future of the European Union on the agenda, Britain's membership of the EU and migration crisis."

Tusk said that "the risk of break up is real. This process is indeed very fragile. Handle with care! What is broken cannot be mended."