Greece is trying to wiggle out of its commitments to bring down its massive budget deficit in two years, wanting to stretch the time period out to four.
But the two biggest economies in Europe, Germany and France, are sending a message to Greece that no extension is viable.
A source close to the French presidency said the two leaders had wanted to have a "straightforward" talk on a host of hot-button topics, from the euro zone to Syria.
Hollande plans to visit Spain on August 31 and Italy in early September, the source said. Both countries have seen their borrowing costs shoot up this summer amid market fears that the euro zone may start to unravel.
Samaras has given interviews to German media stressing that while Athens may seek more time to meet its fiscal targets, it is not asking for more money. But German Finance Minister Wolfgang Schaeuble and others seemed unconvinced.
"More time is not a solution to the problems," Schaeuble said, addressing Samaras' hopes that his country might be given four years instead of two to push through painful economic reforms, to alleviate the impact on the Greek people.
Schaeuble said more time could also mean "more money" and Europe's help for Greece had already "gone to the limits of what is economically viable".
From the sidelines, Dutch Finance Minister Jan Kees De Jager - a staunch ally of Berlin - urged Germany to "stick with its strict position" and giving Greece more time would not help.
European leaders say any decisions on Greece will depend on the report by inspectors from the "troika" - the European Commission, the European Central Bank and the International Monetary Fund.
Samaras is seeking what he calls "a bit of air to breathe" at a moment of rare optimism on financial markets that the EU and ECB are poised for decisive action on the euro debt crisis.
Behind their stern public message, Berlin and Paris may have little choice but to show some flexibility, with little appetite in either capital for forcing Greece out of the euro zone.
Who has who over a barrel in this situation? A Greek exit from the euro is likely to take Spain and perhaps even Italy with it. The euro will not remain viable with 2 of the top 5 economies in Europe using other currencies.
President Samaras knows this and is seeking to play his cards hoping for an extension. But he is not likely to get it. More years probably means more money for the bailout which is politically impossible in Germany and most of the rest of the EU.
So while Germany might allow a tweak or two to the timetable, Merkel will be adamant that deficit targets not slip. This will not sit well with the Greek people who are in a depression and will now be asked to sacrifice even more.