It is also threatening the euro — the common currency used by 17 of its members — and even the structure of the union itself, and is fuelling extremist movements such as Golden Dawn in Greece, which opponents brand as neo-Nazi.
Barroso acknowledged that the current crisis showed the union was "not fully equipped to deal with a crisis of this magnitude."
"We do not have all the instruments for a true and genuine economic union ... so we need to complete our economic and monetary union," he said, adding that the new measures, including on a banking and fiscal union, would be agreed on in coming weeks.
He stressed that despite the crisis all steps taken had been toward "more, not less integration."
Van Rompuy was optimistic saying that EU would come out of the crisis stronger than before. "We want Europe to become again a symbol of hope," he said.
The EU says it will donate the prize money to projects that help children in conflict zones and will double it with EU funds.
The European Union grew from the conviction that ever-closer economic ties would ensure century-old enemies like Germany and France never turned on each other again, starting with the creation in 1951 of the European Coal and Steel Community, declared as "a first step in the federation of Europe."
In 60 years it has grown into a 27-nation bloc with a population of 500 million, with other nations eagerly waiting to join, even as its unity is being threatened by the financial woes.
While there have never been wars inside EU territory, the confederation has not been able to prevent European wars outside its borders. When the deadly Balkans wars erupted in the 1990s, the EU was unable by itself to stop them. It was only with the help of the United States and after over 100,000 lives were lost in Bosnia was peace eventually restored there, and several years later, to Kosovo.