"It's the moment of truth. We have very little time remaining, just a few hours to work through these negotiations," Barnier told the European Parliament in Brussels at the opening of a debate as MEPs met to vote on emergency measures in the event of "no deal".
"There is still a chance of getting an agreement, but the path to such an agreement is very narrow," he added, calling on everyone to assume their responsibilities.
He was speaking ahead of a last-ditch attempt to reach an agreement in talks with his British counterpart David Frost, despite the thorny remaining issues like fisheries.
"The unresolved issues in these few crucial hours that remain at our disposal are fundamental issues for the European Union. We are not asking more nor less than a balance between rights, obligations and reciprocity. Access to market and access to waters are the other way round. No more, no less."
Barnier claimed that, while British companies would retain their rights, EU fishing crews would lose out on guaranteed access. "I don't think it would be fair, nor acceptable, if European fishermen were not allowed, following transitional rights, to have access to those waters," he said.
Barnier said his team was striving for an agreement but "this is not an agreement that we are prepared to sign at any price."
Admitting he could not tell what may happen in the last hours of the negotiations, he called for preparations "for all eventualities".
Later on, the European Parliament adopted contingency measures to ensure basic road and air connections in case no agreement is reached on EU-UK future relations.
Britain left the EU on Jan. 31 and will leave the bloc's single market and customs union at the end of this month, as the transition period will end on Dec. 31. Negotiators from Brussels and London are working round the clock to break the impasse, but no agreement has yet been found.
