Italy and France said there was "not enough progress" on the euro zone debt crisis today.
Fresh market tensions increased pressure on EU leaders to find a way to end the two-year crisis.
"The progress made, including in the governance of the euro zone, is not sufficient and we need to strengthen the weak parts of the system," Mario Monti said during a visit by French President Francois Hollande to Rome.
Markets are waiting with baited breath for a crucial Greek election which may see Athens exit the euro zone.
With just three days to go before Greeks vote to continue with austerity or bring in a party which has promised to tear up the bailout conditions, Monti and Hollande said they hope Greece will stay in the euro zone.
"I want to reaffirm the hope, shared with President Hollande, that Athens will remain in the euro zone and respect its engagements," Monti said.
The reference to the need to tackle governance in the euro zone came after Germany-fuelled calls for a big leap towards further EU integration. Chancellor Angela Merkel had also issued a harsh warning earlier today on the impossibility of Berlin saving the euro zone alone.
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 talks came a week before a key four-way summit at the end of June. Both leaders are pushing for growth and presidential sources in Paris said Hollande has prepared a "road map" which also probes the benefits of pooling debt.
At the talks, Monti and Hollande "exchanged opinions on the hypothesis" of "shared bonds", the Italian leader said. Both Monti and Hollande have expressed interest in a debt-pooling scheme.
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.
The talks came as Spain flounders and fears grow over Greece's fate. The austerity-hit country, which is running out of cash for salaries and pensions, goes to the polls on Sunday in a vote which may see it exit the euro zone.
Monti has been fighting to convince financiers that Italy will not be the next domino to fall in the crisis, but the results of a bond session today proved investors were in doubt.
Earlier, Italy was punished by the bond market today as it struggled to convince investors it will not need a bailout.
The bond auction came just hours before France's Francois Hollande was due in Rome for talks on debt-crisis formulas.
Premier Mario Monti has been fighting hard to convince the international financial community that Italy will not be the next domino to fall in the crisis.
But the results of a bond session proved investors were in doubt.
Rome raised €4.5 billion in medium and longer-term financing but was forced to pay nervous investors much higher rates of return.
The yield on three year bonds rocketed to 5.3% from 3.91% in a similar sale on May 14, while bonds due in 2019 and 2020 went at 6.1% and 6.13%, above the 6% danger level for longer-term funds.
The results were a blow for Italy, which was forced to pay higher rates - 3.972% compared to 2.34% - at a 12-month bond sale yesterday - as debt-crisis sharks begin to circle.