But while Merkel said that there had been “certain progress” at the Brussels meeting thanks to new economic reform proposals by Prime Minister Alexis Tsipras, she said “it has also become clear that there's a lot of work to be done, and time for that is very short".
Any agreement must be reached – and money from the remaining €7.2 billion in Athens' bailout programme begin flowing into Greek coffers – before an International Monetary Fund (IMF) debt repayment falls due on June 30th.
The next round of talks will see eurozone finance ministers meet again on Wednesday.
Tsipras' latest proposals, including tough tax increases and cuts in government spending, arrived in creditors' inboxes late on Sunday night.
There had not been enough time to evaluate them by the time eurozone finance ministers met early on Monday afternoon, meaning that the first of yesterday's high-level Brussels summits ended without result.
But his new €5 billion package of reforms were “accepted as the basis for discussions” at the eurozone leaders' meeting in the evening.
Government sources said the Greeks were now prepared to increase VAT in the tourism sector, abolish many early retirement programmes and introduce a special tax on the wealthy and successful businesses.
German Green party finance spokesman and MP Sven Giegold welcomed the progress, telling Deutschlandfunk “the worst scenario would of course have been for the negotiations to fail. That would have been the worst solution for Greece and Europe”.
With the most recent surveys showing that more than 100 MPs in Merkel's Christian Democratic Union (CDU) parliamentary group were against further bailouts for Greece, the Chancellor may find getting the votes to modify the current deal difficult.
Several other European countries will also have to hold parliamentary votes on any change to Greece's bailout arrangements.