Calling for the 27-nation bloc to reclaim the values of tolerance, solidarity and the common good upon which he said it was built, Monti said Europe was in the grip of a crisis that went far beyond its economic problems.
"This crisis is undermining the foundations of humanism around which Europe was born and developed," he told a conference of religious and political leaders in Bosnia.
"The euro that was a unifying factor ... risked and is still risking maybe paradoxically to become a source of new divisions, of new rifts in Europe," he added.
On Saturday, Monti called for a summit in Rome to discuss divisions fuelled by the eurozone debt crisis.
Such a summit should discuss the rise of anti-European populism, divisions between north and south, and nationalistic prejudices that have been fed by resentment against austerity measures during the almost three-year-old crisis, he said.
Addressing the annual World Meeting for Peace, organised by the Community of Sant' Egidio in Sarajevo this year, Monti said the EU needed to focus on unity.
"It is particularly important when trying to fight the crisis to find the solution, to find the methodology that is uniting people, rather than dividing them," he said.
The former European Commissioner heads a government in Italy that has imposed painful debt-reduction reforms.
There are concerns inside and outside Italy that a new government to be elected in polls next spring could try to renege on some of those reforms however, given increasing public opposition to the economic pain.
Economic suffering across the bloc has seen voters pushed to the left and right and given rise to tensions between northern creditor states and Europe's southern flank, where the crisis first emerged.
European Council President Herman Van Rompuy on Saturday backed Monti's call for a summit on the issue and suggested bringing forward a meeting to foster European integration from its scheduled date in late 2014.