Meeting in Rome, Italian Premier Mario Monti and France's President Francois Hollande stressed more needed to be done to ease market pressures amid black news for Spain, worrying signs in Italy and concern over the upcoming Greek election.
"The progress made, including in the governance of the eurozone, is not sufficient and we need to strengthen the weak parts of the system," Monti said, adding that the views of Italy and France on the crisis were closely linked.
International financial watchers are waiting with bated breath for a crucial Greek election which may see Greece exit the eurozone and could have a knock-on effect on struggling Spain and Italy.
In Athens, with just three days before the vote, thousands of people attended a campaign rally for leftist leader Alexis Tsipras who has promised to rip up bailout conditions that have brought Greece's economy to its knees.
But instead of challenging Brussels, Tsirpas promised if elected to form a government "for all Greeks... with Europe and the euro."
Monti and Hollande said they hope Greece will stay in the eurozone.
"I want to reaffirm the hope, shared with President Hollande, that Athens will remain in the eurozone and respect its engagements," Monti said.
The reference to the need to tackle governance in the eurozone came after Germany-fuelled calls for a big leap towards further EU integration.
Chancellor Angela Merkel had issued a harsh warning earlier Thursday on the impossibility of Berlin saving the eurozone on its own.
"Germany is strong, Germany is an engine of economic growth and a stability anchor in Europe. But Germany's powers are not unlimited," she said in a speech outlining Berlin's position ahead of the June 18-19 G20 meeting in Mexico.
In an attempt to ease the tension, Monti said he knew that "Merkel is continually looking for a solution for Europe" and "is always interested in finding the best answers both on growth and on stability."
The Franco-Italian talks came a week before a key four-way summit with Spain and Germany ahead of EU talks at the end of June.
Hollande described a "road map" he has prepared in light of the European Summit on June 28 and 29 in Brussels, which brings together "growth, stability and the reinforcement of the monetary and economic union."
Monti said he and Hollande had common goals and "exchanged opinions on the hypothesis" of "shared bonds" and discussed "sovereign debt and instruments to re-establish confidence in the most-exposed countries."
But Merkel earlier said that those clamouring for Germany to "pour billions into eurobonds, stability funds, European bank deposit guarantee funds" wanted a quick crisis fix that was unsustainable.
She stressed Europe would only find a way out of the crisis with a strong "political union" with greater fiscal coordination and oversight and insisted "financing growth with new borrowing must stop."
But French Prime Minister Jean-Marc Ayrault, France's number two and a Germanophile, urged Merkel to avoid "simplistic talk," adding: "we need to deal with things seriously and courageously."
While Italy reeled from a painful bond session Thursday, Spain's borrowing costs shattered euro-era records after Moody's downgraded its debt close to junk-bond status and warned of a growing risk of a full-blown bailout.
The eurozone's fourth biggest economy was forced last week to accept a bank bailout of up to 100 billion euros ($126 billion) but it failed to impress the bond markets, which fear the rescue may have added to the Spanish debt problem.
Meanwhile, nerves were stretched to straining point in Greece, which is running out of cash for salaries and pensions and where depression is rife.
Labour Minister Antonis Roupakiotis said that Greece should have enough cash to pay pensions at least for July after the Kathimerini daily said the state only had enough money to pay salaries and pensions until July 20.
Unemployment figures Thursday showed the jobless rate jumped to 22.6 percent in the first quarter, though the Greek stock market closed more than 10.0 percent higher, apparently reflecting an upsurge of confidence.
Greece has already been forced to seek international help twice, first for 110 billion euros in May 2010 and then for 130 billion euros earlier this year plus a 107-billion-euro private debt write-off.