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"The substance is still ahead of us and the discussion will commence next week," Christofias told reporters.
He added he had asked for an extra day before continuing negotiations to examine proposals by the Turkish Cypriot side.
The leaders will have two meetings next week in what Downer said will be an effort to "break the back" of the property issue.
"If they manage to achieve convergence, to break the back of the problem, so to speak, they will have made an important step forward," Downer said after meeting Christofias ahead of Friday's negotiating session.
Turkish Cypriot leader Dervis Eroglu told reporters he expects in depth negotiations next week, before they recess for October due to other commitments.