BRUSSELS — A meeting of European finance ministers broke up late Saturday with no agreement on whether Greece should be granted its third bailout since 2010, reflecting deep divides over whether the Athens government can be trusted to repay huge new loans and leaving the Continent hours from what could be a historic rupture.

The finance ministers planned to reconvene on Sunday, just before European national leaders are scheduled to meet in Brussels for what they have said would be a final decision on whether Greece should qualify for a new aid package, a step aimed at determining whether the country can remain in the euro currency union.

The failure by the finance ministers to reach an agreement, after nearly nine hours of talks, belied the optimism that followed the approval early Saturday by the Greek Parliament of a package of pension cuts, higher taxes and other policy changes long sought by Greece’s international creditors. In a remarkable turnabout, Prime Minister Alexis Tsipras had pushed the package through the legislature despite having led his country into a referendum six days earlier that overwhelmingly rejected much the same terms.

Despite Greece’s capitulation on those terms, many countries came into this weekend’s final round of negotiations skeptical of the Tsipras government’s commitment to seeing through the changes and putting his country on firmer financial footing — and weary of the constant brinkmanship that has characterized the months of negotiations over Greece’s latest crisis.